You outline two paths to innovation here and suggest that it won't take place without these two recipes being followed. Given the innovations that I list above, which took place without your models being followed and which are of huge benefit to humanity, do you still stand by your claims that these are necessary? Do you also stand by your claim that if these two models are not followed "innovation inevitably stagnates"?
There was nothing in my post to suggest that those were the only two paths to innovation. There's nothing implicit or explicit in my post to suggest any exclusivity with those methods. I think they're the most common methods in the modern world. And that any people who don't have them to some degree or another will lag behind.
Invention and innovation will occur to some degree no matter the cultural and economic factors. But if you don't have those proper factors, it will slow down both the rate of invention and implementation. Some people will invent for the sake of invention. If they can't find the investment, its quite possible that their inventions will be small rather than grand. Or that they'll take longer to implement. If there is no system of government enforced patents, you'll still have inventors, just not as many of them because there's less of a profit motive to do so since they know their ideas can be easily copied and co-opted by others, leaving their hard work in the dust.
Some of the greatest works of art in history began to be produced during the Renaissance. Not necessarily because there was a sudden flourishing of talent (although that probably did exist), but because wealthy patrons (church and nobles) sought out and funded artists to create great works. This model continued for a few centuries in music and other forms.
The dot.com boom doesn't occur simply because there are a bunch of college student geniuses on the west coast. It occurs because there are maverick millionaire venture capitalist willing to foot the cash to bring their ideas into reality.
Both corporations and government spend hundreds of billions on R&D to bring new drugs to the market, to pioneer new machines, techniques, and technologies, to achieve breakthroughs in the natural sciences. Are a hundred little collectively owned factories gonna say 'lets spend a few billion on a joint international venture to build a gigantic particle collider?' Probably not.
It takes a concentration of wealth into a limited number of hands to move forward on many of these things. The more hands you have deciding what to do with the money, the less likely you're gonna reach a consensus of 'lets take a risk'. This doesn't say that the elite few are entitled to that money or that they're better or smarter than the lowly factory worker. Some of their investments are bound to be fairly stupid. But if there is enough wealth accumulated in a few hands, they will make investments that will pay off. Ones that any larger group might balk at.
A system that rewards and encourages innovation doesn't mandate that the rich have everything and the poor nothing. But it must ensure that property and wealth can be accumulated in private hands to a significant enough extent to allow for proper investment. I'm fully in favor of a partially redistributive social democracy. But full collective ownership is a recipe for long term stagnation.
(An addendum. Government can absolutely be a tool for innovation, as they are essentially the corporate model I outlined just on a significantly larger scale with some measure of democratic accountability. But if they're the only game in town, you limit yourself again. Because they will inevitably miss some of the ideas and opportunities that a couple million private parties might catch.)