That's a hard problem.
Think of it the opposite way. You just changed your recovery e-mail and password because your recovery e-mail was compromised, and you also used the same password. In other words, you secured your account. Maybe you setup 2FA and a bunch of other things... good.
Now take the place of the attacker. You look at the compromised inbox, see a confirmation email from Google. Nice, you now have an account login, the creation date, and a good password candidate. If you could simply call Google, give the info you already got by reading the compromised mail, and get access, no amount of securing done by the victim could work.
There are two contradicting goals here: keeping your data secure from hackers, and allow some mistakes to be made on your side without you getting screwed (using a weak password is a mistake). Google is constantly juggling between the two and sometimes, the outcome is not what you want it to be.
The solution is not to hold on your personal data too much. Google doesn't ask for it only so that they can target you with ads, even though it is a very important reason to them. It is also used to secure your account.
If you don't want to use Google, good, however, there is no perfect solution, especially if you are not flawless yourself. Keep data on your own machine? Do you have offsite backups? End-to-end encrypted, privacy focused services provide no form of password recovery whatsoever. And services that are a bit too loose may give anyone access with a bit of social engineering. Pick your poison.