Now, I like archers. I even love archers. But they aren't invulnerable. One of the reasons that they work so well against the AI is because it usually creates mediocre units (you don't fight Chosen Archer Warbands with Axemen) and because, well, the AI's an idiot (Once, it tried to send Bowmen across a river and killed them all, leaving the enemy phalanxes pincushions for my Bedouin Archers).

But as I said, archers aren't invulnerable, even elite units such as Chosen Archers and Forresters. Elite cavalry such as Cataphracts or Preatorian Cavalry can rip them apart in a single charge. And even if they survive the first charge, their morale usually plummets and they rout, making them perfect targets for cavalry. Even horse archers, especially Cataphract Archers, can use Cantabrian Circle to kill Chosen Archers with relatively few losses.

Also, although elite archers can fight well in hand-to-hand combat, I find it frustrating to waste them and having to retrain, losing time, money, and experience, especially with non-replenishable mercenary units such as Cretan Archers. Archers are meant to stay behind the lines and shoot at enemies while heavier units such as Chosen Swordmen do their work. When they run out of arrows, quick archers do a great job killing routing infantry. But archers should only be made to force an enemy line as a last resort.

Btw, Spartan Hoplites in loose formation will usually kill Chosen Archers, though at a steep cost.