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.
I agree with the tradeoffs stated here, but I’d argue that any email address you hand out can serve as a unique data point, tied to you.
myusername@gmail.com for obvious reasons.
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.