Yes, although a counterpoint to that is that if these weren't long-standing published problems that have stumped humans, would anyone care? What is important here, the problem/proof, or the fact that they are famous problems that have stumped humans (and therefore make good bragging material).

I'm not sure that a problem being famous, or hard for a human, is the same as it being important.

Take Fermat's last theorem as an example - was a proof of it ever considered to be, then or now, consequential, or was it the Paris Hilton of problems - famous for being famous? A problem whose legend grew because it it so simple to state, with the challenge that there might be a simple proof, and that turned out to be so difficult to solve that it therefore became prestigious to do so?