* The time horizon used to judge incentives vary person to person.
* Willing martyrs exist for various causes. Therefore, it is not just the incentives that matter, but the belief about those incentives.
* Self-sacrifice for others exists (e.g. a mother rushing into a burning building for the chance of saving her children). Therefore, it is not just the incentives that matter, but also the subjective weighting of conflicting incentives.
* A person may spend a great deal of time researching betting patterns for playing craps, none of which can overcome the house's advantage. Therefore, it is not just the incentives that matter, but the knowledge of the outcomes.
* Somebody may work in an oppressive environment for their entire life, rather than changing careers. Therefore, it is not just the effort required that matters, but also the relative amount of effort on different time horizons.
While I agree that incentives are the best way to move population-level behavior, and is usually a good starting point for understanding individual behavior, your categorical statement doesn't have those caveats.
The problem with that system is that the "value" would have to be determined in some independent manner, e.g. an audited cost+ basis, which wouldn't be reflective of the true value of the idea. Granting time-limited monopoly rights allows the idea to be priced via normal market mechanisms, at the cost of high transaction costs.
At any rate, you get the idea. The justification for academic research is that the private sector, supposedly, won't do long term basic science and that grant recipients will. That's a very dubious set of assumptions. We see basic science being done by private labs all over the place, most obviously in AI but also in many other areas of computer science, we see it in the biotech sector, we see it in semiconductor physics etc. The areas where there's no private investment tend also to be the most controversial areas of academia where many people have concluded that the results are systematically useless e.g. social sciences. And meanwhile what we see amongst grant recipients is systematically unscientific behaviour like knowingly publishing claims that aren't actually true, refusing to share data even after promising to do so, accepting unvalidated modelling as 'science' and a million other things.
Most problems in academia come down to bad incentives. Researchers are incentivised to publish for prestige and citations, which are poor proxies for improving our understanding of the world around us.