There have been attempts in this direction, it's absolutely doable to use a shared seed where many people contribute a random value.
However ultimately a different approach was chosen that solves the same problem: You don't choose an arbitrary curve, instead you define a set of properties that you want your curve to have, based on security, speed and ease of implementation. Then you end up picking the very first curve that fulfils that property.
That's how Curve25519 was created. There's very little wiggle room in there.
Also it should be said that the hypothesies of choosing a "bad" curve that noone can spot are very hypothetical. We know these NIST curves have an unexplained random seed, but noone has an idea how this could've been used for a backdoor.
However ultimately a different approach was chosen that solves the same problem: You don't choose an arbitrary curve, instead you define a set of properties that you want your curve to have, based on security, speed and ease of implementation. Then you end up picking the very first curve that fulfils that property.
That's how Curve25519 was created. There's very little wiggle room in there.
Also it should be said that the hypothesies of choosing a "bad" curve that noone can spot are very hypothetical. We know these NIST curves have an unexplained random seed, but noone has an idea how this could've been used for a backdoor.