Piracy is obviously the main reason.
Other than that, in the beginning when my collection was really small, I wanted to expend my consoles' capabilities by having all those wonderful homebrew apps. Seriously, what people can come up with is pretty insane and most of the time really rewarding. As the collection grew, I kinda dropped the emulation since right now I pretty much have all the consoles I need (and some more). I still emulate those that I don't have access to and with the latest XBOX 360 and PS3 Slim acquisitions, I think I'll save up some money for the Switch successor when it comes out. The only games I can not play are exclusive to PS4/PS5 and XBOX One/Series, provided there are any notable ones.
Other than consoles, I've installed homebrew apps on my girlfriend's LG and my Samsung TV, just so that we can have ad-free YouTube.