In order to trade, the buyer delivers cash and the seller delivers shares. Imagine it's a short sale between banks. The buyer institution doesn't keep all of its assets in cash (no interest accumulation that way), so it has a division whose job it is to rent out treasuries overnight for cash to cover liquidity needs. The seller institution, meanwhile, has to go get some shares. By the way, shares can be acquired in a few different ways, each of which would be managed by a different group within the institution (stock loan, swaps, options, etc).

That doesn't even take into account the clearing aspect of the trade, where a separate corporation has to do the bookkeeping that says that Firm A sold a share short (shorts++) and Firm B bought a share long (longs++). Or wait, did Firm B cover an existing short (shorts--)? In the status quo, these numbers net out and get updated daily. But real-time settlement would require far more memory writes, so to speak.

In the end, I don't know if the nicety of real-time settlement is all that nice. You'd essentially have to either (A) make the entire system so fast that the existing process can take place instantaneously and so robust that it can happen millions of times a day, or (B) create an entirely new (blockchain?) methodology for clearing.