I really don't see that ever happening.
First, with more and more functions being moved to the processor, the chip maker who can pack more into the CPU will use a socket that provides all necessary lanes to the rest of the system. Socket 7 had what, around 300 pins? Now they have over a thousand? They keep getting bigger and bigger.
Also, Cyrix and WinChip probably had no choice but to make chips that used that socket, if they had any hopes of selling chips. If a new company wanted to break into the mainstream CPU market, they probably would have to produce chips that used either an Intel or AMD socket currently in use. They would have a tough time getting motherboard manufacturers to make something special for them. Of course, today I suspect everything is so patented it would be impossible.