> Or do they tag things and say "Customer X signed up on this date, so he is bound by T&C number 12, whereas this other customer signed up a year later and is bound by T&C number 13". That seems unwieldy since there is a common infrastructure.

If the company would like their T&C to carry the force of a binding contract upon me, then yes, keeping track of my agreement seems like the absolute bare minimum they must do.

Either these things are real contracts or they are not. The idea that it's too onerous for a company to keep track of its contractual agreements is absurd. That's giving them all the benefits of a real contract with none of the obligations.