People that don’t want to work will suddenly become engaged in the political process? Sounds like work to me.

In addition to the people who don't want to work, there's the people who can't work (due to disabilities, family care responsibilities, discrimination in the workplace etc.), and the people who could get more done without a job in the private sector (volunteers, artists, and... politicians!).

The kinds of people who would benefit from UBI in this way are often the people least qualified or capable of engaging in politics. (Though in general, the credentialed class is full of people who don't understand the philosophical presuppositions either. The failure of education.)