Please don't always send an email. A malicious person can now start signing up every day with a bunch of emails resulting in users who do have an account receiving an email from your site daily/hourly saying "we noticed you're trying to sign up again". At which point they become annoyed with your service and either unsubscribe or delete their account.

Hotmail do this everytime someone tries to reset my password which happens almost daily as I have what turns out to be an account name that is in demand and it's really irritating. And there is nothing I can do to stop someone attempting to reset my password - I have 2 factor switched on so they won't be successful.

Of course you can add more logic in to try and be more intelligent about when the emails are sent, but most sites won't get this right when they can't even store passwords correctly.