In a Nutshell:
Hizb ut-Tahrir does not adopt democratic elections as their method or a style in their method when seeking power as it is not in line with the method of the Prophet (saw).
There is a fundamental problem
those who adopt such approaches fail to identify.
Election campaigning requires backing and sponsorship from elites and every sponsor has vested interests. More often than not, their interests don't align with the Islamic movement leading to a conflict of interest, creating circumstances where compromise becomes inevitable.
Otherwise, it escalates to clashes and ultimately dissolution or annihilation. And it is the fear of utter annihilation that drives people to compromise. Compromise has been the key factor why every Islamic movement has been derailed and/or thwarted over the past century.
Democratic parties remain at the mercy of an elite class whose interests lie in maintaining the status quo, wealth, power and authority. Democratic Parties that don't comply with the interest of the elites either fade into obscurity or are outlawed and dissolved. Or in some cases, they try to sponsor themselves by trying to establish their own sources of funding but ultimately they become the very thing they set out to change.
If elections could changed the system and its vested interests, it would be banned.