1Password tells you which of your passwords have been part of a breach. Many other companies will suspend the accounts of anyone whose login information to
their leaked as part of another site's breach.
Other websites won't allow you to use a password that's listed as a common password from the aggregated passwords in breaches.
Lots of studies have been done on password frequency, such as the top 100 most common passwords and what security people can do about their repeated use.
Based on your question however, I'm concerned you don't actually get my point. You're being forced into action, exactly how companies are forced into action, by the availability of this information. You have to change your password if it's easily available to anyone who uses this API and who has your email address, you no longer get to pretend it's not a big deal.
