Not every single item of clothing has its own verb - it's rather a group of items, like footwear, headwear, jewelry etc. For example, גורב is used both for socks and stockings, which are quite different. So, specifying the item is necessary, in order to avoid confusion. The same goes for other verbs.
That’s not true I’m afraid and in this aspect there’s no difference between modern Hebrew and Hebrew from 2000-3000 years ago (possibly before that it was only pronounced as b but we don’t have much evidence from that time).
Generally the rule is that ב is b at the start of a syllable and v at the end of a syllable, with certain exceptions.
gé-reV - sock - גרב
gar-Bá-yim - socks - גרביים