Edit: Sorry, I say it way too much, but this merits a repeat of the one-liner: "The reason God was able to finish the earth in only six days is that He didn't have to worry about backward compatibility [or legacy system integration, or satisfying an installed userbase]."
I think it would be way harder to trade a basket of stocks (e.g. pairs trading, going long one and short the other) if you had to worry about mismatched settlement dates across the different stocks; it would be like trading spot against a one-day forward.
But in some ways exchanges also function as a natural monopoly; especially for primary issuance. e.g. look at AMEX's IPO slate compared to the big two, where the market is right now - it's insignificant, and they are the #3 exchange in the US. People want to list to make money, and that means going where the liquidity is until there's a really good reason not to, like with NASDAQ's move to electronic trading in the '70s.