It was the other way around for me. But regardless, the best part of owning your own domain - if you don't like your mail provider, just change the MX records to a new one.
Heck, I could run my own mail server if I wanted (been there, don't want to go there again, but could if I really HAD to).
I didn't use the migration, so can't speak to that. I just had to set up the DNS entries on my domain. Granted, there are a fair few (MX, TXT, SPF, SRV, A, CNAME..), but there's good documentation and it only took me about 30 minutes to set everything up.
Of course, I only have one account (lastname@personaldomain.com) and therefore didn't have to deal with setting up multiple users, migrating data etc. I also set up 2FA for my account.
I did all this over one weekend (from looking at different providers, to signing up for O365, configuring etc), and haven't had to touch anything since. The only question I had was related to billing (I went from a month-to-month to a yearly account) and that was answered quickly by a real human being.
Another choice is Office365. I use my own domain, with O365 providing the email services. I pay $60 a year for the cheapest plan (with Exchange). I migrated from Google over a year ago, and have slowly moved all my accounts to my new email. It's not something you can do overnight, but if you stick to it, it's not hard to do.
One time I had a question, I was able to use the web interface to request support, and a real human called me back in 10 minutes. It wasn't a very complex question, so I can't say if he was super knowledgeable, but he certainly seemed like he knew the platform, and was able to answer my question in just a few minutes.
Oh, and I know this is a throwaway account, but I'm not a shill for MS. This is just my personal experience with O365, and YMMV - it's worked well enough for me.
Microsoft will happily send you up a creek if you are a large paying enterprise. Don't think you'll get useful support if you pay $60 a year. Their cloud stuff breaks all the time and the typical support offer is to wait and see if it's better tomorrow.
Heck, I could run my own mail server if I wanted (been there, don't want to go there again, but could if I really HAD to).