Ah, I see. I have a PC hooked up to my TV, which I use for the purposes mentioned in my post. I (perhaps erroneously) took it for granted that most people using these programs were doing the same.

This is probably beside the point, but thinking back, XBMC made a lot of sense back in 2003 when it was released. It wasn't as feasible to a) have an entire spare PC and b) hook it up to the TV easily. I certainly didn't have HDMI or even VGA on my TV back then, only composite and maybe component analog video...

I use a beamer instead of a tv but it is not complicated to dedicate a small computer like a gigayte brix or an old laptop and use the tv/beamer as the screen. Be it with kodi or using regular apps doesn't make a huge difference these days. With the advent of hidpi monitors, all modern OSes support scaling the icons/text/widgets so it is perfectly viewable from a few meters of distance.

I use a wireless keyboard+trackpad combo as a remote which I leave out of the way inside my living room table when not in use.

I recommend using an HDMI cable. The inconvenience of threading a cable across the room is massively outweighed by the convenience of never having to deal with network issues, limited bandwidth, or introducing additional software issues you didn't already have before.

Besides the gaming desktop, and the two laptops, I also have a normal old school desktop for the TV.

And honestly, I don't see why that's not a common practice. Super easy to use.

No Android fiddling needed at all.

Why not just cast from your cellphone to Chromecast / AppleTV (free AirScreen app for Chromecast devices to accept signal from apple devices)