I also had the old US B1/B2 visa valid for multiple entries indefinitely. For a few years after the expiry of the passport it was in, I was able to continue to use it by showing the new passport along with the visa in the old one. But one day it was refused at Heathrow – huge inconvenience as it meant I could not fly pure and simple, and lost that trip completely (BA did however refund my full fare, as it was flexible).
I did quite a lot of digging, because I was so annoyed, and the position appeared to be that the US authorities changed the rules so that to be valid, a visa had to be (a) unexpired – naturally – and (b) in an unexpired passport. (b) was the new condition and was tied up with tightening of rules after 9/11 And nowadays of course their ESTA premits are only valid for 2 years anyway.
I guess “indefinitely” on our visas actually meant “undefinitely until or unless we change the rules”. Which realistically a state must be allowed to do!