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.
Also, with DTC there is a continuous net settlement system that basically nets a brokers transactions together for the day and basically lets them know which securities are credited or debited from their account and how much they need to pay or receive for the day. It helps solve the issue of high speed trading and nets each brokers obligations out at the end of each day. In its simplest form if a broker had two customers and Customer A sold a share of AAPL and Customer B bought 2 shares of AAPL. The CNS system would basically net those two transactions together and calculates that the broker is going to receive 1 share and that they will pay x amount of dollars.
There is definitely room for improvement because sales don't settle till T+3 (however the settlement cycle is shortening to T+2 as of Sept 5th)
You're assuming the blockchain would work similar to Bitcoin, where every 'trade' (transfer) is a settlement, written into the blockchain. While this is the holy grail, you've rightly pointed out issues with high-frequency trading, synchronization across nodes, etc. The current system does T+3 due to this. A 'blockchain' could conceivably do better - even if it doesn't record every single trade like Bitcoin, it might record transfers at better granularity and better frequency.
What's wrong with off-chain transactions? Off-chain transactions have the same value/worth/weight of on-chain transactions. Both transactions are worthless before "settlement" (which is 1, 3 or 6 confirmations depending on how careful you are) but after settlement they are practically the same.
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.