Far better to just get rid of them: Headers first makes most reasons obsolete. The circus above doesn't really help, since it's using the chain itself, which of course checkpoints distort the selection of, so it's just circular.
Old checkpoints distort the selection of the chain, but there's no reason new checkpoints can't be done with network consensus on chain long after a previous checkpoint (thus its more bootstrapping than circular). It's potentially a powerful new way to compress the history and bring new nodes up to speed fast, especially since you can include a utxo patricia tree hash in there too.
From what I understand, headers first doesn't affect the new full node sync time at all. Please correct me if I'm wrong