There's a pretty good argument to be made that the opposite happens in practice especially in terms of any meaningful innovation. It's also worth noting that a lot the innovation is outright harmful. For example, stuff like planned obsolescence, adware, and user tracking are all examples of harmful innovation driven by capitalism.

It's also worth noting that USSR managed to go from being an agrarian society to first in space without any need for capitalism. It was consistently innovative and had many world firsts under its belt.