A name I've seen in connection with this issue is Obtainium. From a cursory look, it appears this just streamlines checking for and getting apk's from GitHub release pages and other project-specific sources, rather than adding any trust. So maybe it just greases the slippery slope :)

Security guidelines for mobile phones, and therefore policies enforced by large organizations (think Bring-Your-Own-Device), are likely to say that one may only install apps from the platform-provided official source, such as the Play Store for Android or the Apple App Store for iOS. You might say it's an institutionalized form of "put[ting] too much trust in claims of authority." Or you might say that it's a formal cession of the job of establishing software trustworthiness to the platform vendors, at the mere expense of agency for users on those platforms.

People are not taught how to verify the authenticity and legitimacy of software

Rant: Mobile computing as we know it is founded on the rounding off of the rough corner of user agency, in order to reduce the amount users need to know in order to be successful, and to provide the assurances other players need, such as device vendors, employers, banks, advertisers, governments, and copyright holders. See The Coming War on General Computation, Cory Doctorow, 2011. Within such a framework, the user is not a trustworthy party, so the user's opinion of authenticity and legitimacy, however well informed, doesn't matter.