The "stock exchange" is already decentralized [0]. It has been this way since electronic trading really took off on... i think Instinet (now NASDAQ) and Archipelago (now NYSE ARCA) in the 1990's. The National Market System [1] is a piece of legislation from 2005 that attempts to unify the markets from a customer's perspective, but it is a very leaky abstraction. That said, it is interesting to see what happens with any new exchange.

[0] https://www.sec.gov/divisions/marketreg/mrexchanges.shtml [1] https://en.m.wikipedia.org/wiki/Regulation_NMS