If everything were centralised yes. But many of these are transactions that also happen at 3rd parties so they are not in the stock exchange, and that is why some equities take 2 days to clear. These are separate ledgers. Centralising gives the stock exchange total control over everything and 3rd parties are often not for that. A centralised system means all control is central, 3rd parties could be locked out, have no control over escalating costs, etc.

Centralised control was very much the mainframe era of operations (or possibly that is actually coming back with cloud computing now) but many things have decentralised for good reasons. I am not at all a fan of centralised systems having total control over costs, lock-out, access to my data, etc.