“Is there a way to do what you're suggesting with identities”
There are certainly solutions, but I don’t know what the best solution is, hence why I called it an open problem.
An example solution would be something like having your identity be a hash of your initial public keyset, making each key have a set expiration date, adding new keys by signing them with one of the existing keys, and then storing all of the rotation operations in a transparency log.
“the only way to solve this without centralized providers is with blockchains”
That’s not true; you probably want a transparency log, but that doesn’t require blockchains.