

For data leaks, haveibeenpwned only requires your email, and they send you a notification if it ever shows up. They don’t actually check passwords.
Unfortunately there’s no secondary info linked with a license plate that makes doing this sort of notification private without just downloading the full database locally.

The sort of information they could gather from a site like this would be a list of license plates that somebody is worried about being tracked. I can think of several government organizations who would love that sort of information right now.
It’s a sort of Streisand effect