We're so used to setting webapps do this that we take this for granted, but Gmail was the first email webapp to do this. It's possible it was the first webapp, period, to do this; I feel like Gmail's use of XmlHttpRequest was innovative at the time.
Fast forward twenty years, and what about Gmail is innovative today? Nothing that I can think of. It's mediocre (there are lots of filtering improvements they could make that they aren't making, for example), and everything that made it good has been copied by other webmail clients. There's no particular reason except momentum to stay on Gmail.