It’s an email account, not social media so I think this is a ridiculous take. It’s inherently private and only shared with people you explicitly send it to, such as family.

For all you know they may not turn out to keep being your daughter forever. It’s kind of a gross overstepping of parental boundaries

Such a shoehorned, irrelevant point that won’t apply to 99% of the population. This sounds like a you problem that you’re projecting onto others, and it’s honestly rude to say that it’s a gross overstepping of parental boundaries.