I'm not sure I completely follow you, but there's nothing preventing a party from making use of the legal system or contracts or whatever in addition to a blockchain.

I still think that making some common classes of dispute impossible is highly valuable.

Which classes of dispute does blockchain make impossible? It can attest that a key signed a particular transaction, but that doesn't necessarily mean it was done by or intended by the owner. General purpose computer security just isn't quite good enough for that, that's why smartcards and secure enclaves exists.