It wont work because gov has no interest in not knowing which service the user is trying to authenticate themself to, it is in its interest to connect these informations. We see exactly these attempts every 2-4 years in the eu parliament.

i suspect it's a matter of how you sell the idea of this service to the governments.

i agree that the usual overreach will stand in the way, but i feel (perhaps wrongly) that the idea hasn't been pitched in earnest.