The problem is, the ONLY curves that are supported in practice are NIST P-256 (prime256v1) and P-384 (secp384r1), which aren't considered safe. So, I guess, many are reluctant to switch (because we're non-experts and don't know real implications, but we heard that there's something not right there - and shouldn't one be wary?).
Neither Curve25519 nor Curve448 - which are said to be safe - are usable with X.509 and TLS, yet. Still waiting for that RFC to get past the draft status.
So, what should we do?