Rotating DH groups periodically is difficult. SSHv2, for example, has support for this. It takes a lot of computation to generate new groups, but then how do the client and server agree on a group? Well, the server tells the client, and the client has to like it -- i.e., the client has to trust the server's group. This isn't better than just having a bigger nothing-up-my-sleeves group to begin with.

That, ultimately, has been the solution the community landed at: nothing-up-my-sleeve curves for ECDH and EdDSA.

The nothing-up-my-sleeve part is all about setting / agreeing to obvious and hard guidelines for generating and selecting curves before doing the selection, then you can see that a curve was generated and selected without any hidden agendas. We have several of these now that are generally thought to be secure, though, of course, it's hard to say for sure. It's a pretty good outcome.