Correction: Bitcoin is an example of why the market can produce everything that is needed.
Yes. How much did Satoshi sell the use of his invention for by the way?
"Markets" properly understood are voluntary trading environments. Bitcoin was built voluntarily by individuals pursuing their own interests and using their own resources and property (some of those interests being profit, or eduction, or ideology, or experimentation, etc.). The fact that the creator didn't "sell" the idea is irrelevant.
Bitcoin would NOT have been an example of free market innovation if it had been produced via taxation and coercion (ie - by a government diktat or program). Big difference.
I don't think anyone has said that government is in the business of invention.
Although US government defense expenditure on technology research can be thanked for this conversation.
Governments did not invent locomotives, but decades after the invention of the railway governments all over the world spent taxes laying tracks and buying rolling stock. So what, why is that bad? People need transport, people pay taxes, why not taxes build the transport people need? Still a matter of paying for stuff, what's the gripe? Paying for evil things like napalming children ok yes, definitely sucks. It's like the argument the NRA uses about guns really...
Governments don't kill people, politicians do. It's a matter of where you point it and why. Government is just a machine made of taxes. Some thing's it's good at, other things better left to free-enterprise.
Either way it's still the market as in many cases government is Customer and/or Employer #1. So what.