Paying up front becomes a problem if the flight school folds, as flight schools are wont to do.
You then find yourself at the end of a rather long line of creditors, with little possibility of recouping all your money. That said, it is advice most commonly given to people who are about to embark on an integrated training course, where you would laying down up to 70 odd grand, and would be with that organisation for 12 months plus, and hence be exposed to risk for that long. If you get the Hughes Guide to becoming a pilot, it is something he seems to repeat every few pages, and in bold type!