I agree with all of this. The example of the patent on steam engines is fascinating, thank you! It's certainly true government granted monopolies are far from the ideal incentive structure, with many downsides. (And lobbying for EG patent extensions likely IS rent-seeking). Advance market commitments and other systems likely have better characteristics.
I was rather objecting to the misuse of a technical term, and the idea that we should expect all innovation to happen without reasonable incentives.
Rent-seeking has a technical definition; earning money from things you invented does not meet it. While Salk is obviously an inspiring example, a wise society should happily incentivize the development of useful technology.
I'm not sure that argument is rigorous enough to be called a proof. We have no guarantee that the S&P 500 will grow faster than world wealth.
It's plausible it will, but one could reasonably purchase something like gold or BTC to hedge against scenarios where it doesn't.