I realise that it's not what you want to hear, but it already exists in multiple ways:

- Use your own domain

- Tell GMail to forward all your emails somewhere else

- You can even allow e.g. Yahoo to send emails on behalf of e.g. your GMail address

It seems to me that your frustration comes from one single problem you have, that you mentioned in a comment:

> I still haven't managed to move everything away from my old gmail because sometimes it's impossible without recreating some accounts from scratch.

The emails sent by those accounts to your GMail address can be automatically forwarded to your personal domain, so this is not a problem. Therefore I am guessing that your frustration is that you still have to use your @gmail.com as a username on those websites.

And this is not an email problem at all: it's just those websites preventing you from changing your id (/username).

At the end of the day, the perfect solution to this problem is to have your own domain. Those of us who "screwed up" by not doing it 20 years ago have to deal with it (which is honestly not a very big deal), and we should teach the new generations that they should really have their own domain :-).