First, should you always do a wrap when you are knitting a short row, or only when the pattern specifies it? ...What is the purpose of the wrap?
There are some instances where you don't have to wrap. I've heard it's feasible with garter but I wrap on garter, as well. In most instances the wrap prevents a hole from forming. There are also several diff ways to do short rows, with some variation on W&T, where there isn't a 'wrap.' (I think Stanley's 'Knitter's Handbook' has three techniques for short rows but only one includes a wrap.)