Used to do this. I had issues with either the audio or the video feed randomly dying, though, so I ended up finding a way to make HDMI+USB work when I moved.

More reliable, but now that I'm starting to think about reorganizing my office, copper will no longer do for 4K120 as that'll go over the 5-meter limit. And an optical high bandwidth HDMI+USB setup isn't cheap.

Upsides and downsides...

TL;DR: yep

I use steam remote play. I've got a mini pc in my garage, another in my living room, and a third in my bedroom. There's CAT 6 between my office and bedroom but the rest is wireless.

I spent more than I had to because I wanted all of them to be able to play less intense games like Hollow Knight and some emulation locally so if I have family and friends over we can have 3 games going at a time.

It's one of the few PC tinkering projects I've taken on outside of work in the last several years because I've grown to mostly hate it. But this was super satisfying because I ended up with something that I could enjoy alone and with family.

I beat Shadow of the Erdtree on the one in the living room so it can't be too terrible. I probably wouldn't advise it for anyone wanting to play competitively but for casual gamers, couch co-op, RPGs, or friendly online games I can highly recommend this kind of setup.

I love Moonlight. I just switched over to Linux and haven't gotten my Moonlight host set up yet. But it's on my to-do list. What do you use to stream it? I'm rocking a Powkiddy RGB30. The square screen squishes stuff a little, but it's pretty cool to play Astroneer on something so tiny.