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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.

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But if you do, and take unreflectedly the results of computer science about computability for granted, you may get wrong conclusions.

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.

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