I also want to point out: if the main impediment is the ability to play games comfortably with a controller on TV, my wife and I are currently playing Cyberpunl 2077, modded, on a TV, in a different room of the house, using a playstation 5 controller.
both Steam Link and Apollo/Moonlight (I found Apollo's setup of virtual displays out of the box to bw superior) work very well.