How do I turn off "subscribe by email" for guests without affecting registered users?

This appears to be a default functionality in the actions widget for at least blogs, possibly for other content.

I'm concerned if I disable 'subscribe to blog' in the actions that registered users, and members will not be able to subscribe to the blog for notifications, because there's no distinction here between allowing 'everyone' to subscribe by supplying their e-mail address, versus a registered user or member.

Further, where are these e-mail addresses stored? If it's not against a registered user, that means that they haven't ticked a box agreeing to be contacted and that they cannot manage their subscription. We then have their personally identifiable information and that becomes a data privacy and GDPR concern.

I'm hoping the answer is stated somewhere, is a simple option in an extension, and that this is easy to disable across the multitude of applications we have en mass.