These days, getting an email or other sign-up for something has (at least) two significant factors:
* Do I trust you with the data I give you; and
* What do I get in return for my data?
If you are clear and upfront that the sign-up has been introduced because of lots of bogus accesses, you'll gain some sympathy. But people will still ask both of those questions.
If you act in a trustworthy manner, and you provide value in return, then I think it's fine to ask for a sign-up. But you need to gain the user's trust, both that you will treat their data with respect, and that there will be something in return.
Exactly how you convince them of those two things is not easy, and effectively "marketing".