Driving with a dog in your lap

so then my question- if there is an actual law to prohibit dog on lap, would that still be contrary to " public policy" ? ( allowing carriers to insert an exclusion )

There's all sorts of laws regulating driving - I'd venture the guess that a very high percentage of auto-liability claims come with some violation/citation by the insured driver, whether it be failure to yield, failure to maintain control, etc.

It doesn't impact liability coverage.