I think consolidating the weapon skills is a great idea, and as was mentioned previously - anyone keen on "individualizing" people will not a problem. In any case; YOU were the person who gave them a weapon arbitrarily in the beginning, right? Why is that less silly? I make sure every single one of my soldiers are trained in EVERYTHING, then I give them selective tasks. If one dies, his position is either temporarily reinstated (if he is important enough) by one of his squadmates, or I find another person to train.
Personally I never saw much use in having to train every weapon skill individually; but I did like the idea of practising "sniping" and so forth. I'd rather have it called "Long Range Combat" and "Close Quarters Combat" than burst and snipe though; as that would allow for a broader spectrum of possibilities (for example; the further back in your squad you are, the less effective a person with high "close quarters" skill would get, whereas a "long range" squadmember with poor "close quarters" would find it difficult to hit anything from the front. Perhaps a damage bonus/multiplier should be in place if you are at the very tip or the very back of your squad, depending on your skill?
Obviously the squadmember would use whichever skill he would be most efficient with in his position (but perhaps there could be a roll on tactical [I found a use for tactical! Woo!] and intelligence?).