With Google SSO you will always be dependent on their services, if they get down, they get hacked (which is very unlikely at the moment, but things might change) or someone compromises your google account you will be lost.
Very much this. I see users getting locked out of Google account often, or Google changing their policies (like the recent change of free G Suite accounts to premium ones) which would mean you'd be locked out of most accounts.
Are there big email providers, maybe paid, where potentially should be more reliable. Meaning at least they have a customer-service and you will not get locked out by the script?
With Google SSO you will always be dependent on their services, if they get down, they get hacked (which is very unlikely at the moment, but things might change) or someone compromises your google account you will be lost.