As always it is more complicated than that, certainly there are people who file with a fake SSN or ITIN and some who do not. I am not sure how you would know someones status and be able to separate the amount paid into categories, I suppose you could infer but it is a bit like the numbers here undocumented, no one knows.
Certainly for Federal taxes most would not earn enough to pay significant taxes and there are deductions, I remember reading about how people claimed dodgy dependents overseas but it was years ago and forget the details.
And of course if there is a subsequent route, say you legalise through marriage to a USC you can transfer your past payments to your legit SSN.
The big taxes that most people can't avoid are things like sales and property taxes.
In the County I am currently sitting in a few months back there was an ICE raid on a Mexican restaurant, big fuss in the local rag and social media. Anyway according to the local paper which is very Progressive 30% no show the following day at the local schools. And I am pretty sure none of them would have been on F1 visas. Cost per pupil is $13k.
Odd thing is that Immigration is Federal but the costs mainly fall at a local level.