Am I misreading something, or can you only use a *@hey.com address and not your own domain? So if Hey lock you out you potentially lose access to all of the accounts you set up using that address. PayPal can't send their 1 time code, your bank can't reset your login. Your password manager can't do 2fa. If you own the domain you can switch there dns to someone else and regain your life. If you don't own the domain to your main email you are running a risk I wouldn't run.
This is a valid concern with using any third party mail provider. Even if you own the domain though, you probably use a domain provider, for which it would be un-wise to use your own domain as the login email. Do you really have full ownership of any email address?