The problem is metal defenders - specifically enemy axes. Even axes are weaker there than bows, and so are swords.
Well, axes versus axes you break even with the melee bonuses.... so 5 v 5, without considering things that apply to the longbows also.
Generally I think breaking even is more than satisfactory if you have dealt collateral damage.
But perhaps there is a case for replacing all swordsmen and replacing them with longbowmen(surely,with little penalty,you can get the beaker benefit of skipping IW, if you have copper and feudalism. With no copper either and just feud, skipping IW is more circumstantial).
The generally purposes for swords are:
Kill archers (better than axes against them)
Kill catapults (they will be fully healthy, and axes lose to them more often)
Then mounted units, i suppose...
But against AI swords are basically a specialist unit, only better in that space when all the axes are weak enough that the axes won't defend against a sword instead of the archers. Or in cases where the enemy has no metal.
Longbows can do all the swords can, and then defend your cities better later against elephants and the like, while you reconstruct your new invasion force with elephants, macemen, etc.
However I don't think they easily replace the role of axemen, who are 70% cheaper, meaning you have more catapults for the same cost army.