This kind of invalid curve attack exists against all elliptic curves, so it's a bit difficult to argue that they're a reason to prefer one curve type over another.

The situation is a bit different in the presence of point compression, in which case you're typically concerned with twist security, but the security of the NIST P-256 quadratic twist is pretty decent, so again this isn't a strong argument against it.

The two good reasons to choose something like Curve25519 over NIST P-256 are 1/ speed and 2/ the fact that it's somewhat simpler to obtain side-channel protected implementations. For SSH key exchange, it's pretty much a wash for most realistic settings (only a server that spends significant CPU time simply establishing SSH connections would care about the performance difference here).