Ah, you sound like you are not fuzzy on your history, so I will defer to your take on it, with one distinction: the Battle of New Orleans was not fought open-field style. The US Army established positions behind fortified positions (such as cottonbales) and slaughtered the incoming troops.
Quite right. However, Andy’s maneuvering was what forced the British into a position where they had to attack a fortification.
Had someone else been in command the Brits would almost certainly have taken the city.