The thing that home computers, PC's and HiFi and TV electronics have in common is, usually, having their connections at the back and occasionally front. Trying to get an R-Pi into an aesthetically good looking box under the TV with no PCB mounting holes, and without a mass of wires in all directions is certainly a challenge, definitely not boring, but a struggle I'd have preferred to do without !
Yes, we could do without. However, an acceptable compromise would be to turn the microUSB power plug 90 degrees to let it face the same edge as the hdmi plug. That will leave the west edge free except for the SD card, but you are rarely going to touch that one once settled.
I guess 95% of us currently around won't touch the composite, so that can stay inside a box being inaccessible. The audio out is very, very easy to route to one of the two other edges (south, east) if needed.
So if only we can get the microUSB turned 90 degrees we are down to a two-edge layout, which is acceptable.
Unfortunately that still means having HDMI and LAN/USB on adjacent sides. Though in all honesty that's no worse than having them front and back if the board isn't large enough to reach both front and back of the chosen case !
Power, RCA Video, Audio and USB seem reasonably easy to relocate by flying-wire and sockets on stripboard. LAN could be relocated the same way but I think that requires removing the LAN jack as it has magnetics included - a short RJ45 cable to socket without magnetics included is probably easiest. It's all a pain but not impossible (*).
As HDMI is difficult to relocate, that dictates it is at the back and how I think I'm going to do it. It also allows SD card access from the side which is tolerable. I'd add an image but can't figure out how and probably more on-topic for the case threads.
(*) I'm intrigued how people proposing tablets of some form or other plan to deal with the R-Pi form factor and connector poistions but that's also off-topic.