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.