So I have T-Mobile (a prepaid account on a pay-as-you-go plan with no data), and there's already a parental control feature: they call it Web Guard. It's been there for a long time (since dumbphones) and is set to "Young Adult (17+)" by default. To turn it off I need to provide age verification: my full name, address, date of birth, and last four digits of my social security number. Although this information "will not be collected or stored for any use by T-Mobile USA" -- presumably it's only sent to Equifax or some other identity verification partner -- I'm still not comfortable giving them that information (I believe the only personal information I've ever provided is my name, email address, and ZIP code). I haven't made a fuss because I have no data plan, so turning it off won't help me, but I do still find it annoying.
Incidentally, when I went looking for the setting today (it's in your account profile under Phone Controls), I discovered I now have a Binge On setting, which is (of course) on by default. However, I haven't checked to see if streaming video works (even though I have no data plan).