What connection do you think a third party is saving when using openid? Generally speaking the only thing the third party needs is your identifier which in most cases is just an email. It's no more devastating for the user base for that information to be leaked than it is when they're handling authorization themselves. I personally think using a government backed authorization platform is a terrible idea and something completely liable to be abused by those in power, but it would objectively be better than trying to have every single service store your personally identifiable information themselves.