"someone broke into my house at exactly [time]. Can you track their license plate and track them down"

Sounds reasonable, but most police departments will not do this, even if the data is available to them and running the query is easy.

They will tell you to file a report, preferably online, which will then be incorporated in local stats, and may also be useful in your interactions with your insurance company.

But they will not do anything to help your specific case.

Okay, but they should. Putting up barriers like warrants would make it less likely they do something.