Innovation occurs from imagination. It grows from public buy-in. Do you think the Super Soaker water gun occurred from necessity? Necessity didn't bring forth the internal combustion engine, the internal combustion engine was around as a rich boy's toy until a capitalist found a way to make more money from it. The wheel was invented in South America. It never made it past the toy stage because necessity didn't have a use for it up in the Andes. They really could have used it in North America, but necessity never thought it proper to bring it about there.
I think people like Edison, Bell, Branson, Dyson, Gates, and Martin Cooper (inventor of the cell phone) might dispute your assertion that gov't is necessary for innovation.
You're actually going to pit China & Russia's post WW2 innovation against that of the West??
Firstly, crap like the super soaker isn't innovation, it's a pointless by-product of others innovation. Most innovation, if not all, from the market place has it's roots in research done at institutions like NASA. Where does Apple get it's glass for it's touch screen wonder? NASA research. Where does improved battery life come from? Research at NASA. New plastics? Research at NASA.
All of those inventors just found marketable uses for research, normally scientific, conducted by inquisitive individuals not after wealth but after understanding.
No of course, I'm not going to pit Chinese or USSR innovation above the west. But they had their moments.