That is flatly false. Worker cooperatives are every bit as innovative as any other form of private corporation. These are owned by workers not a centralized government. There are quite a few of them and you may well have purchased their products with it even realizing it. Two additional examples you may have encountered are Equal Exchange and King Arthur Flour.
There aren't more of them because they have a hell of a time securing financing when most businesses are financed through equity sales which they can't do.
Example of innovation please. I’ve seen first hand that no collective farm is able to produce nor SpaceX nor even EV nor even plant in time and harvest in time.
I'm not close enough to manufacturing to evaluate how innovative their approaches to factory automation are, but it's not like they're based solely on turnips:
The collective farm that produced SpaceX is the United States Government. It carried out all the research and development necessary to create and further the North American space program. And it is existential in furthering it to this day. Without this source of contracts, research projects and income SpaceX would not be able to produce its commercial spin-off products.
It looks like this system was created out of necessity; there was no viable product for what they needed. Necessity is the mother of innovation after all, and we find this sorts of innovation frequently in non-collectivized entrepreneurships as well. Still, very cool!
By this logic capitalism is the thing holding back capitalist farms from being rocket makers too? Or do you only apply it when you get to use the word "collective"?
Of course it is the logic of collective. In capitalism you decide how you'd want to spend your resources, on a farm or on a rocket. In collective it is collective who decides.
There are multiple Kibbutz in Israel that plant and harvest on time and are the major source of innovation for Israel's AgTech sector (which is only behind the US in terms successful startups).
There aren't more of them because they have a hell of a time securing financing when most businesses are financed through equity sales which they can't do.