Well people here are talking about "carbon" deposits, what type? Are they dry sooty deposits from a rich mixtures or oily deposits from burning oil?
A simple plug reading should point to the cause.
While most everything you say is true, but the ecm can be programed in any manner the designer determines and as long as the vehicle can pass gov emsioon standards, they're good. I've been by-passing those shit tunes for years.
My point was that with modern cars you don't get rich mixtures except for first 5-10 seconds with cold engines when ECU goes open loop waiting for O2 sensor to heat up so it can measure correctly. After that ECU goes lean and stays lean with the mixture, at least with modern petrol engines. With such engines you can get deposits only with buring oil, which, as @blueone explained, is solved with air-oil separators.