[yomismoaqui]

"There are privacy implications as the email transmission informs the mail service the applications the user is using and when they used them."

Not really, as I can enter any email on a service login page that uses magic links for auth. The owner of that email will receive the login link but that doesn't mean they tried to login on that system.

[Y_Y]

Not really indeed. You're right that false positive are possible with such a system, but false negatives are not. That means that you're leaking information about when a user didn't use a service, as well as partial information about when the did (which you could combine with other data to tell you something meaningful).