> If we solve NP-complete efficiently then we may break TSP and all sorts of magical optimisation problems joyously drop out of the sky at our feet. It is not clear if this would also break integer factorisation and thus RSA, but perhaps it might.

Not true. Factorization is NP, so having a fast way of solving NP-complete problem would yield a way to solve factorization as well. On the contrary it is not known to be NP-complete (and is believed to not be), so solving factorization in polynomial time would not help with other NP problems.