Reprocessing works fine in practice, as others have mentioned, it’s uncommon because it’s politically unpopular. Partially because everything related to nuclear anything is politically unpopular, partially because having high-purity plutonium lying around poses nuclear weapon proliferation risks. Though this can be avoided by breeding and reacting in situ.

> why is there so much nuclear waste that has not been bred and reprocessed?

You may be inclined to wonder why there is so much nuclear waste at all. After all, we could just melt it, dilute it into a slag with a bunch of silicon, cart it off to a boat and dump it into a deep ocean trench if we wanted to be safely rid of it. But we don’t want to be rid of it. It’s extremely expensive to produce and extremely valuable, and any permanent solution for storing nuclear waste needs to be reversible in case we ever want it back for reprocessing.

>If this were a solved problem why is there so much nuclear waste that has not been bred and reprocessed?

Because naysayers have had a dominant influence over nuclear policy since Chernobyl.

Because reprocessing is problematic politically, not technically. Yes, reprocessing involves some ridiculous chemistry, but we know how to deal with it. What we don't have is political will, especially when anti-nuclear activists are joined hand-in-hand with war mongers crying about nuclear weapons if anyone tries to go for plutonium economy (France and Japan are considerable way there).