Why the universal Turing machine simulation in O(TlogT) cannot be applied to transform multi-taped Turing machine into single-taped?
Just because that UTM itself requires $2$ tapes to do its task that efficient. Removing one tape, the magic is gone.

But assuming you have the fantasy power to do efficient $1$-tape simulation, what gains do we have then?

That should be the question rather than your question.