Shaft109, what you were taught is the standard military circuit. I can see many advantages to it but not that many disadvantages, myself, though perhaps others will come up with ideas. Principal benefits:
a. it keeps the circuits small and within the ATZ;
b. as a result most of the circuit is within gliding range of the runway or at least the airfield if it all goes quiet;
c. more circuits per hour = cheaper training.
OTOH there are fewer 'slots' in the circuit at once, but then that hardly matters if you can do one every 4 minutes (my average at home base).
Tim