OP here. What would be the advantages of moving to fastmail.com instead of staying with my Dreamhost-hosted email? What do they do better than those hosting providers that also provide email? Since I already pay Dreamhost for hosting, what would justify the extra $5/month? Are they inherently more secure?

A lot of people are commenting on owning your own email and having backups. Perhaps a compromise solution would be to have Gmail handle my domain email? I won't get rid of the advertisement/parsing, but at least I would be able to migrate to something else if they ever for some reason block my account, and I would keep their top-level security and anti-spam services. I don't know...