That's the real problem. The state doesn't actively police insurance policies. All that's needed is a policy when the vehicle is registered. It can be cancelled a minute after.
Insurance was (the only) one place that Vermont did things right. When a policy was cancelled the insurance company forwards the notification to the state. If the plates weren't surrendered within a small number of days, the state police come looking for them with a big fine or, if that doesn't work, a warrant. Deadbeats need not drive.
Because we have some net worth, I have to protect myself on both ends. My wife was hit a few years ago. My wife had police reports putting the other driver at fault. The other driver tried to sue _us_ because we did have insurance and assets (she didn't). Our insurance company had to pay our damages plus fight her off her claims. No problem, the police said that she was a serial litigant but without a "real" under/no insurance policy it would have been even more of a mess. Insurance companies have lotsa lawyers.
I had 100/300/100 until about 20 years ago, then went to 300/300/300 and a $M umbrella. I figure it's good to make sure that the insurance company has a good deal of skin in the game. Umbrella policies are pretty cheap, comparatively.
Yes, full coverage. My truck is a '13 and my wife's car is a '19. I'd normally drop a nine-year old vehicle but everything, with wheels that turn, is worth real money these days.