That doesn't really make sense? If you used an address on your own domain, other people would be pretty unlikely to enter that email address instead of their own. The problem with misaddressed email should be limited to domains with really high username density; nobody else than the Gmails and Outlooks of the world need to solve the problem because nobody else also has the problem.
For example, email clients generally allow you to use multiple accounts at the same time. Configure your client to read emails from both accounts at the same time, and any time an important email arrives at the legacy account try to update the sender.
(I mean, I'm sure that xkcd.com/1172 applies, but still this seems like an odd thing to be blocked by.)
I'd rather begrudgingly keep taking advantage of Google's spam filter over adopting the added workflow branch that is perceivably likely to trail me for another decade-plus.
My name is common in certain areas, and I consistently get transactional email from banks, telecoms, and insurance companies around the world.
These businesses do not verify that their customer’s email is truly their own prior to sending emails.
Framing custom domains as the solution to this problem is a bit rash, no?