There are numerous ways it can play out depending on the way each state structures their liability laws but imagine your child turns 16, you forget or "forget" to add them to your policy, and they are involved in a serious accident.
In some states the insurance company is on the hook because everyone at a residence is covered under the policy unless listed as excluded. The insurance company has no way to collect on any premium uprate that might have occurred had you listed them on the policy. And they might have recourse to come after you. And they could cancel your policy.
In other states the insurance company could retroactively cancel your policy for failure to list a driver leaving you with the liability from the accident.
In some states the insurance company is on the hook because everyone at a residence is covered under the policy unless listed as excluded. The insurance company has no way to collect on any premium uprate that might have occurred had you listed them on the policy. And they might have recourse to come after you. And they could cancel your policy.
In other states the insurance company could retroactively cancel your policy for failure to list a driver leaving you with the liability from the accident.