The good thing about PCs is that you can build them as big and small as you want, and even put quiet fans in them.
There was a time when a SNES in the living room was ugly, but today it's a sign of beauty. Many people hate the way the US SNES looks, but I prefer it. Some people like their computers to be an RGB light show and others don't. Again, you can build the PC however you want if it doesn't match the style of your living room.
Yep. That's my point. A gaming computer is as big or small as you want it (within limits) but given the options on the market these days making it look the part should be manageable. But, I get it that "the wife" might not care as much about the look but because it is a computer and not mentally what she might want in the living room. Easier to fool her if it is a smaller, stylized box that you call a "media player".