Its only really a few more turns to hook up axemen and they stay useful for some time and the early survivors then have promotions that can be used later. Early on, after the others have archers, an archer with a promo is pretty useless. Also even on prince the AI get archers very early and it only takes one to mess up your three, and if on a hill forget it, a few axemen still stand a chance.
I gather from old threads lots of people, including myself, never bother with archery or horseback riding until its a one turn research or usually a throwaway part of a later tech deal.
Those early turns you spend doing archery for very limited usage inded are much better used else where, as the agg civ may then get axes before you and then you are in trouble. Also unless you have used world builder before to scope out and can place all the copper, revealing copper later means a civ may stuff you by settling on it before you do, again big trouble...
just some reasons the archer rush isn't talked about...