If you would like the perspective of a low time student pilot.... I must say I would find that instruction difficult. I am not aware of a formal definition of 'short final', but if it is much less than say 2.5 miles when I would be particularly low and slow, I don't think it could be safely executed in many places without powering-up gaining significant height. I presume the implication of such an instruction is not to climb?? There are several of examples of people dying as a result of pressured manoevers like that in the pattern. A mile further out, and it would be no issue at all, but in those last few minutes when I am shedding speed and height, fiddling with flaps and radio, I would not be happy with such a request, in fact I hope I would reply 'unable', and request plan C.
Why would ATC not ask for a go-around?