Everything is great, until you get in an accident....
A minor fender bender, the insurance company will probably never notice. But a claim with a potential big payout (100% your fault, totaled your car killed a pedestrian and destroyed 3 brand new cars parked in a lot)? The insurance company is going to do everything they can to not pay that claim. Knowingly falsifying information on your insurance forms is enough for them to deny a claim.
I know more than a couple people whos claims were denied when they had their cars registered and insured at a vacation home in florida or south carolina, then crashed in NY. The insurance companies have well paid investigators to find out why your car which is registered and insured in Rochester got into an accident two blocks from your "other home" in staten island. When they find out you live their 10 months of the year and that car only makes a few weekend trips to the summer home upstate, you're done...
EZ pass records, license plate readers, traffic cams are all available in a lawsuit... Its not hard to figure out where and when your car was at a location.
Do people do it all the time? yup. Do insurance companies deny claims all the time? yup.
Is it worth it? in my mind? no.
Put your kid on their own insurance policy, and put their car in their name. It may cost more, but at least it removes their faults from your insurance and keeps your assets safe. Your kid crashes into someone, they can come after your house, savings and retirement savings if its under your name and insurance.