See jwz's struggles with hosting his own email. (Not linking to his blog here with HN as the referrer...)
With email, the 800 lb gorillas won, and in the end it didn't even solve the spam problem.
So a 20 pound monkey can also throw around some weight. To be fair I only use it for personal stuff its probably different if you need enterprise scale l.
I have a 15+ year old Gmail account that I've used everywhere. Spam has been a non issue since 15+ years ago.
The only Gmail accounts that are "overrun by spam" are those of people subscribing to lots of spammy newsletters and then not knowing how to unsubscribe from them (or figuring they'd stay subscribed in case the next newsletter is the Magical One™). But that's 100% self inflicted and you can't save those people with any technical solution.
Email spam isn't a day to day problem for Gmail (at least) since Bayesian email filtering was first implemented.