The problem with Dole was that there was not one single central ledger of stock transactions that was being kept updated in real time.

Would blockchain have solved that? It's centralized in that there is one ledger. But natively resolving and publishing transactions at high speed is not a feature of blockchains yet. A centrally managed ledger without distributed calculations would be way faster.

Also worth noting that Dole was a weird enough case to be news-worthy, and that it was ultimately resolved. I think it takes more than a few edge cases to justify completely rebuilding the entire basis for a major part of the global financial ecosystem.