Power factor for transformers

PF depends on leakage inductance of xfm and the load itself.

 

relatively small leakage inductance of xfm + operation near rated load point

 

The no-load transformer p.f. is low [approx.0.1]. However, a transformer does not change much the load p.f.Since the active no-load power and reactive no-load power are low the load power factor [at full load] does not decrease more than 2% [usually].
Of course, if the load will be low the p.f. could decrease more [up to 0.1 at no-load!].

 

Another extreme case is a short circuit case where I>>I_nom. PF also low.

 

That's a bit ambiguous question.
I'd suggest the source from which you extracted that tidbit was suggesting that it is usual practice to use power transformers at reasonably highPF because:
Z of transformer is largely inductive
Draw your phasors..
When PF of load is unity,what is phase angle between applied voltage and I X Z drop in transformer?
When PF of load is zero, what is that angle?

At high PF your transformer I X Z drop is at right angle to applied voltage so doesn't change it much, because the hypotenuse and long side of a right triangle are nearly the same when vertex angle is small. That's elementary geometry.
At zero PF that I X Z drop Is in phase with applied voltage and subtracts or adds to it volt for volt.

So you'll get better regulation with a load having reasonably high PF.