It’s not really “the only way”. A similar problem to think about would be: what if your primary email account got compromised?

It makes sense to set up alternative means for recovering any account (or changing the associated email address), for example via second mail address, phone number, one-time-passwords, snail mail or similar. Many account providers use a recovery question system - here, I’d suggest using irregular answers, e.g. for “what is your favorite colour”, I would’t use a colour at all to make it harder to guess.

Compartmentalizing would be another approach: use different providers in a mix so that when one goes the way of the dodo, parts of your registered accounts remain useable. Ideally, for “critical” stuff like bank accounts, you’d split them up between different email addresses. But then again, for this kind of account, I’d really expect the bank to provide some other ways of backup access/restoration.