Thanks. I came up with that myself although I would like to see if someone can poke holes on it [1]. I am aware that many NP-hard problems, for example, usually have good approximate solutions in non-pathological cases. So that could be a big hole in that argument.

Could a theoretical computer scientist give more insight on this? In particular, what is the hardness of approximate solutions to most problems that could have strong impact in the real world?

[1] I did, in passing, find a similar idea discussed somewhere afterwards. If someone has a reference for that, I would be glad to have it.