Capital is not required for innovation. See Open Source, Cuba's CimaVax, the Soviet space program.
Open source is a good example of where innovation can work because all it takes is people donating their time. It doesn't require $15 million of rocket fuel and a $100 million rocket to make a commit to Linux.
Government-backed research works well when there is no immediate commercially useful aspect (e.g. basic sciences, space exploration), but it's incredibly bloated and slow compared to business R&D that has competition and motivation to make discoveries.
Where are the socialist programs producing processors competitive with Intel/AMD? Where is the socialist program producing an electric car people want more than Teslas?