I installed this type of AC in my house when I moved, but have 2 units, one in my PC room and one in large living room/kitchen that's in the center of the house. Honestly, the PC room unit isn't very useful and I could have saved money with just the one unit in the center of the house, it's a new house so it has good insulation so just having that unit run will cool the entire house down and I can just turn it on every now and then even when it's really hot outside. Does cost a bunch more than the mobile ones(although a good part of that was the installation costs) but it generates no noise and probably consume less energy too, don't regret the investment, it's both useful for gaming and sleeping during summer. Can also be used to heat during winter if you need to.
But yeah at some point I thought about drilling a hole in the wall and just running cables through the house to have my PC in another room. In fact I may still do that later on, to reduce noise. Need somewhat long cables for keyboard/mouse/screen/sound, but you can bundle them and hide them in some cover thing so doesn't look too bad, or I might run them through the attic instead(less ugly, but a lot more annoying to go run that shit and need even longer cables and any issue with the cable would be a big pain in the dick to fix). At the time I decided on checking water cooling out instead and it's a decent fix, but doing watercooling on GFX cards is also somewhat annoying and have to be redone every build which is also annoying, and it still generates noise, while a cable setup would be a one time thing.