How does carb heat increase the risk of dirt ingestion?
Carb heat is not only about heating the air going into the carb, it's also a meant to be an alternate air path in case the air intake becomes fouled or the air filter gets clogged by debris, snow or ice. Fuel injected airplane engines typically have an alternate air intake that bypasses the air filter for the same reason, it's part of the checklist to test the alternate air. 

The reason there isn't a separate filter for the carburetor heat air is that the same thing that clogged up the main filter could clog up the secondary, it's better to have unfiltered air for a short time than take the chance of losing your engine.