It’s a great option, but it’s debatable whether or not it’s privacy improving. On one hand it’s your domain. You don’t need to worry about moving email services, and as you control it, you can have as many addresses as you want. One for each service, catch all, and so on. On the other hand it’s YOUR domain. Only you have access to it. It’s quite easy to filter out the first part, before the @ sign, and identify exactly who you are. It’s a unique data point, tied to you. It’s arguably as bad as handing out a phone number.
The bit about moving email services can help privacy indirectly at least.. If a provider no longer meets your privacy needs you can move to another that does.
That’s much harder when you don’t have your own personal domain
myusername+token@gmail.com — easy to filter out the plus and everything after, and it’s very likely more people use this format than uniqueusername@my-own-domain.com, making more likely that this filtering would actually be automatically applied.
What about email relays? Kdhrbrk@mozmail.com doesn't seem like it could be tied to me, then firefox relay forwards the email to my actual email address.
Yeah, email relays are probably better. I wasn’t necessarily considering those in my comment. But there are tradeoffs there too; now all your incoming mail can be read by a 3rd party, and there’s one more server between you and your email that needs to be up and working for you to properly receive mail.
This is very useful for identifying which services might have sold your email to third parties.
Another downside may be that once you're using your domain for emails, you better make sure you don't accidentally let it expire or mess up some configuration and start missing emails, which may be important, sent to you