Functionally yes, the plan is in the parent's name. But at least where I'm from, you already have plans that are geared at kids, e.g. they have limits on how big their bill can be so they don't blow it up, certain services are turned off for them such as pay-per-minute calls, and so forth. Perhaps to put a different way, the carriers might not have this info right now, but it would be straightforward to implement this limit this way. Any other approach that I can think of would be both more technical work and also a bigger breach of privacy.