[frederikb]

This (partly) exists for some mobile carriers.

I know of at least one carrier, but is only usable for their own customer self care portals/apps. There it is possible to auto-login to their app if it is accessed via their network and not via Wi-Fi. For security reasons only a limited amount of functionality is accessible. Neither customer data can be changed nor can any actions resulting in additional cost (buying packs / options) be performed without additional authentication mechanism of a higher security level (auto-login via SMS or use of a password).

The MSISDN is only added to the HTTP request internally in their secure network and never exposed externally.