I will say it is imposed by the carrier. Not just for YouTube, but Netflix and all other streaming services.
There are plans carriers sell you that only allow standard definition, for now they tend to give you the option to turn it off which most average consumer don't bother with.
On T-Mobile, 'Binge On' is enabled by default, all videos you streams will be reduced to 480p but with the benefit you don't use up your data.
AT&T, if you read their unlimited choice plan, it's locked to 480p streaming:
https://www.att.com/plans/unlimited-data-plans.html
For Cricket Wireless:
Cricket will apply Stream More automatically to your Unlimited plan (including promotionally priced versions), but it will not affect your data speed, except that with Stream More turned on, certain higher definition videos will stream at standard definition quality, similar to DVD (about 480p). Customers who steam higher-definition video will consume less data with Steam More turned on.
I think the fact that if you're using these plans with the 480p restriction and your YouTube app on Android can override it while on cellular data has more to do with the discrepancy in the software of the phone, ideally the carriers wants to limit you. Or I could be wrong and the restriction API is is baked into the YouTube app itself and not working correctly on iOS.