Many of the really large spammers seek out large domains, like the "free" ones, precisely because they are large.
Smaller custom domains are less interesting to spammers, because the target counts are small.
You won't see anywhere near the spam you see today once you switch to using a custom domain of your choosing.
This is one of the many hidden benefits of using smaller and more professional domains for email service.
In addition, the service also has great spam blocking and filtering, just as you would expect.