No, a "blockchain" wouldn't help. It wouldn't help finding the holders of three years ago. Also, putting all stock transactions for the entire market into one blockchain would have huge traffic and synchronization issues. All the players have to agree on transaction order. You'd have one giant file that was petabytes long. If you used one of those schemes that "summarizes" the blockchain, you wouldn't have an authoritative record of who owned something years ago.
Bitcoin only works because transactions are few and slow transaction commit is acceptable. Most schemes for scaling Bitcoin involve "off-chain transactions".
DTIC predates high-speed trading. It was designed when it was assume that if you bought a stock, you'd probably hold it for weeks or months, not seconds or minutes.