Given the way any provider can lock you out at any time using your own domain is absolutely worth it.
I've found if you use something like firstname@lastname.tld people generally get it if they've dealt with any other business email addresses (in some cases it actually makes you appear more professional). They usually have your first and last names before you get onto email addresses so they can piece it together and validate it.
If you're really worried about password resets showing your domain get a second domain and only use that for online transactions, it can then be as obscure as you like. Sure there's an extra cost to that but it's a trade off of cost vs the level of privacy you want.
I've found if you use something like firstname@lastname.tld people generally get it if they've dealt with any other business email addresses (in some cases it actually makes you appear more professional). They usually have your first and last names before you get onto email addresses so they can piece it together and validate it.
If you're really worried about password resets showing your domain get a second domain and only use that for online transactions, it can then be as obscure as you like. Sure there's an extra cost to that but it's a trade off of cost vs the level of privacy you want.