Historical Artifacts

Conaidering that you won't stand stiff and upright as an unmoving target, but rather bent in the knees like you see modern fighters, as well as moving around, hitting the knees or feet is gonna be a lot harder. You'd have to bend down to reach for them, putting your own head and neck deeper within the enemy's reach.

The fingers are also hard to hit (but not impossible), but mostly they're hard to armor if you want to retain flexibility. The same goes for the face: You need to be able to see what's happening and what the enemy is doing. Armoring either would probably bring more drawbacks than protections.

That's not to say there are no ways to armor these parts, but they might not have been invented at the time or simply too complex and expensive to make. If they found that a ton of people died with chopped-off fingers, they'd find a way to armor those. If they never bothered, it probably won't have been worth the cost.

If you're interested in the decisions that go into selecting armor, I recommend this blog entry by an ancient historian as well as the follow-up where he uses the logic laid out in the first post to be pedantic about pop culture examples. The blog is, after all, named "A Collection Of Unmitigated Pedantry" (and I can really recommend it in general).

It's suggested that the term "Achilles' heel", meaning a seemingly insignificant point of fatal weakness, comes from exactly your observation of the Dendra Panoply, an armour of exactly the same period as Achilles and the Trojan War.

Modern armour has similar drawbacks.