This summary of the America/Iranian academic Vali Nasr's work (which appears in the "Oxford History of Islam") answers the question really well:
Independence ended the sovereignty of European powers over Muslim territories; however, it did not produce states afresh. Despite the rhetoric of planting of new seeds, new states were nothing more than new branches based on a trunk planted during the colonial days.
Colonial institutions, policies and attitudes towards governance determined the direction of the postcolonial nation-state, all developing in the European intellectual, legal and cultural legacy. The machinery of the colonial state was inherited and to varying degrees the model of the colonial state was followed with ideological continuities visible despite the rhetoric of the new leaders. Colonial power ensured all discourse be both hegemonic over and repressive of the Islamic world. It was not a dialogue between equals nor a conversation, but an attempt to reconstitute Islam and Muslims both at the level of consciousness and at the social level.
The impact of this historical experience is not difficult to discern and has been highlighted by numerous researchers.Nation-States
Colonization started with India, the scramble for Africa and the division of Ottoman lands following World War I. Islam received harsh criticism from the colonialists and their scholars instilling a sense of inferiority in the local elites and rising bureaucrats including those who opposed colonialism. For Muslims with a world outlook, territorial limitations had been irrelevant. Colonial territories did little to unify their peoples to create national societies or cultures, with focus in defending territories against other colonial powers, with promotion of the sanctity of boundaries leading to permanent borders.
This prevented lasting identities seen the diverseness and tensions in Lebanon, Iraq, Indonesia and Nigeria. Loyalty was moved from universal to territorial values, with deliberate manipulation of diversities resulting in increasingly fractured societies, with tensions and wars inevitable - Sudan, Iraq, Malaysia, Pakistan, Nigeria and Chad etc. Territorial disputes involved Morocco, Algeria, Iran, Iraq, Syria, Lebanon, Palestine, Malaysia and Singapore. Education
The colonizers encouraged and invested in education and educational institutions for those who would run the machinery of state. Over time, they influenced generations of Muslim leaders and intellectual developments in the Muslim lands. Famous institutions included University of Punjab, University of Malaya and Atchison College in Lahore.
The elite sent their sons to schools in Eton, Harrow, Oxford and Cambridge in England or in Paris and Amsterdam. Iqbal studied at Cambridge and Heidelberg Universities as well as Lincoln's Inn where Jinnah received his law degree. Many of the North African liberation movement leaders were students in North African French schools and Paris Universities. Amongst the militaries, officers would be trained at places such as Sandhurst and Saint Cyr or officer schools modelled on European counter parts such as Quetta Staff College in Pakistan.
The pervasive impact of education introduced the Muslim world to western literature and philosophy. Figures such as J S Mill and Rousseau and over time, Sartre and Camus, became models for dissenting intellectuals just as Lenin, Castro, Mao and Che Guevara captured the imagination of activists. State Institutions
The colonial state was highly centralised utilising institutions with a European flavour; the police, judiciary, military and bureaucracy being key repositories of its authority. Institutions were not designed for society - for instance, the bureaucracy was designed not to maintain order but to ensure the smooth running of government and economy. This structure allowed a European minority to rule vast territories, managing the economic flow of resources and goods between the parent state and its territories.
These institutions, embedded in subsequent states determined the basis of state, its character, relationship with society and other states. Pakistan for instance replicated the colonial state in role and function, with Jinnah the first governor-general and the India Act of 1935 being law of the land until 1956. In Turkey, the law was secularized based on the Napoleonic Code, the script Latinized, polygamy prohibited and the constitution amended to remove "Turkey was an Islamic state". Security
Security forces were trained to provide support to their colonial masters. The training ensured soldiers and importantly the officer corp, internalized the values of the colonialist, resulting in an over-preoccupation with order and impatience with politics of the masses. Militaries were trained not for external war but for preservation of internal order, giving them a perceived right to interfere in politics to restore order. The size of the militaries was usually based on interests of the colonisers and Muslim states inherited omnipotent militaries, too large for their population sizes and economic strengths.
The colonial policy of recruiting amongst minorities was due to their closeness with the colonial order and willingness to suppress the dominant community and unresponsiveness to religious calls like Jihad. The Great Indian Mutiny of 1857 influenced thinking resulting in Alawis dominating the Syrian army and Punjabis in the Pakistani army.
The forces having fought with their colonial officers up to independence institutionalised attitudes of mistrust and cynicism of those who fought for independence. Indonesian generals remained wary of Sukarno, removing him with the pretext of Communism, like those who lead coups in Bangladesh, Nigeria and Sudan. Even left-leaning junior officers who overthrew their old-school senior officers in the anti-imperialist struggles did not resolve tensions between military and civilian orders, leading to military takeovers in Egypt, Libya, Iraq and Syria. Economy
The importance of certain geographic locations to colonising powers (e.g., North West India to the British for supply of troops) or where the colonisers arrived late (e.g., the French agricultural relationships with Syria) meant they developed patronage networks, leaving indelible marks in state-society relationships. The state emerged as paternalistic and society came to see patronage as its function (the Malays remaining aloof from economics and commerce expecting the state to guarantee economic standing). Bureaucracy
Like the military, the bureaucracy was moulded in the ethos of colonial culture, sharing the same political outlook. Due to their power over the state machinery, politicians would have little control over them lest they disrupt the workings of state.
As such, they had major input into state formation, ensuring continuities in the ethos and mode of operation of the state before and after independence. In Pakistan the bureaucracy eclipsed the political elite in managing the country, replacing Muhammed Ali Jinnah and Liaqat Ali Khan after 1951 by senior bureaucrats Ghulam and Iskandar, both having risen through the bureaucracy under the British. Judiciary
The British colonies generally had a system of justice modelled after Britain, with some degree of autonomy, its independence from the executive branch becoming embedded in the postcolonial state. As such, colonial subjects usually had respect for it. In Pakistan, the judiciary regularly defied the executive branch - opposition to Ayub Khan's banning of Jamaati Islam in 1964 and Ghulam Khan's dismissing of the government in 1993 and most recently the stand-off against Musharraf. The Malaysian judiciary has a similar history as do most British territories. Governance (Politics of Identity)
Colonial rule was often through manipulation of divisions: ethnic, linguistic and religious. By accentuating social differences, they were institutionalised by different treatment of communities in law, at polling booths, resource allocation, recognition of religious rights etc. This encouraged the politics of identity at the cost of development of uniform civil societies. In India, the All-India Muslim League in 1906 lobbied for separate electorates for Muslims and Hindus with similar reactions in Malaysia, Nigeria and Palestine. Authority
Colonial administrators varying rule over vassal populations accounted for the different experiences in state formations. In Algeria and Libya colonial rule was direct while in Morocco, Tunisia, Malaysia and India local elites were used. The Dutch in Java, utilised the local elites to resolve labour shortages, entrenching socio-political positions, creating dependencies between the peasantry and elite (the Dutch permitting exploitation and impoverishment for their own ends).
The British carefully controlled 250 princes controlling a third of the Indian population - control of the rest by manipulation of landowners, local chiefs and grandees. Symbiotic relationships resulted, entrenching the positions of local elites, who favoured compartmentalisation of policy in favour of a uniform political arena. This allowed them to control their polity and negotiate with the centre, still visible in Pakistan with landowning classes controlling politics and resisting land reforms and the power of monarchy in the Gulf States and tribal chiefs in East Africa and Nigeria. The Algerians with direct French rule to ensure integration into France and exploitation through commercial gain for their settlers resulted in centralised rule. Conclusion
Colonialism's structural expressions continue to reproduce themselves in a fashion that perpetuates this power relationship. Elites in most Islamic countries are largely products of superimposed structures wherein lies the essence of the polarization between elites and masses in the Muslim world. Muslim intellectuals, imbued with the Western discourse of rationality, entered political life as natural allies to the local elites and the colonialists.
The masses had no choice but to fall back on the values of their own society to protect themselves from the new class that sought to pattern life along Western lines.