The PSTV generally has issues with updates or connectivity, but when it works it's roughly the same quality on my 720p projector as the switch and the steam link. And there's the answer to "why not just play the Playstation directly?" - in order to get sound that's synchronized with the screen, you need a way to get the video from the sound bar area where the playstation lives to the projector, which is a dozen feet away, on the ceiling. With the switch, the dock is next to the projector, and bluetooth sends audio fast enough for 99% of switch games. Steam link has built in BT as well. Sony doesn't. long range HDMI cables cost more than the PSTV did, so there's all the answers anyone could want.
When, once or twice a month i want to sit on the most comfortable chair in my house and play a game, it's the switch. I also try my best to only buy games with cartridges unless there's a serious sale and i have a gift card.