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I am not assuming that at all.

You think RSA (the inventors) would have kept RSA (the algorithm) secret, had they not been able to patent it? I think you're mistaken.

The history of software/algorithm patents is a history of technologies with limited adoption and/or interop problems until the patents expired. Patents are more likely to kill the future of a technology than to promote the technology.

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By assuming RSA would be invented without patents, you are begging the question. Would R, S and A even be employed by MIT and given free reign to do their research if MIT was not assured of capturing the rewards of their innovation? I think you'll find there are a negligible a number of institutions who will invest in anything without prospects of getting returns on it, much less risky enterprises like research.

now we see your next assumption is that investment into R&D happens without incentives. It doesn't.

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