frostbite, I was thinking much the same. It's sometimes possible to remove the pins from the plugs if you can prise in the locking tab with a tiny screwdriver, but then you would have to carefully mark all 21 of them so they went back in the same place! You also have to consider moulded-on mains plugs. New sets will need HDMI cables - it just gets worse...
If you can get through the wall cavity then a possibility would be to make a large enough slotted hole and fit something like a cooker outlet plate over it to make a neat cable entry/exit.
Or just hide all the cables with a large pot plant!