No, I don't think it should have.
Arguably, acid-proof armor would be better in quality and harder to get than standard non-acid proof armor. Going by some of the established Predator culture, you do not give cocky hormonally-high teens expensive gear meant for pros knowing that they stand a good chance of dying anyway; it would be a waste of resources. On a more down to earth level, in a video game, you don't immediately get the best stuff, you have to earn/buy/find/steal/aquire it as you advance. This would also be why the Preds didn't have the guns to begin with, they had to work their way through the hell of a pyramid and find them before the aliens grew too overwhelming for them (though admitably, the idea is still somewhat silly). Nothing that hasn't already been said, of course. The spears and the ceremonial dagger were the exceptions because arguably, you would still have to give the kids SOME chance of making it out alive.
I am not saying I'm satisfied with Anderson and his AVP, but he and his crew were not stupid enough to have unintentionally mix-matched acid and non-acid proof gear.