With infinity resources our computers would be universal Turing machines.
Personally, I think that is sufficient to call something a Turing machine even if it has limited resources in reality. After all you can't have infinite tape.
I don't simply take results from CS without some reflections on how they work in a physically limited turing machine, that would be silly, so my conclusions are usually right.
Computers are still universal Turing machines because an infinite-tape computation[1] can be subdivided into an infinite sequence of finite-tape computations.
[1] Meaning a computation using an arbitrarily-long tape, since by definition a computation is finite or its result is undefined.
Personally, I think that is sufficient to call something a Turing machine even if it has limited resources in reality. After all you can't have infinite tape.