Regardless of its origin, its usage in context clearly implies it's supposed to be understood as a non-standard, non-default process. Making preferred software design choices feel like defaults, or making preferred app or distribution ecosystems feel like default is the product of extraordinary and intentional effort to set expectations, and so I don't see it as an accident that the nomenclature would be used for the purposes you describe.
I did make a comment in this thread about the historical usage of the term sideload, although for my purposes, I was noting a historical quirk frim a unique time in the history of the internet rather than disputing any premise in your post. It was the first and only comment at the time I posted it and I was not anticipating such an unfortunate backlash that seized on terminology for the purpose of disputing your point, or for otherwise missing your point.
But it is indeed missing the point. Requiring developer registration to install is exercising a degree of control over the software ecosystem that's fundamentally out of step with something I regard as a pretty important and fundamental ideal in how software is able to be accessed and used.