"Vegetables are cheap."
pedant (n.) 1580s, "schoolmaster," from Middle French pédant (1560s) or directly from Italian pedante, literally "teacher, schoolmaster," a word of uncertain origin, apparently an alteration of Late Latin paedagogantem (nominative paedagogans), present participle of paedagogare (see pedagogue). Meaning "person who trumpets minor points of learning, one who overrates learning or lays undue stress on exact knowledge of details or trifles as compared with large matters or general principles" is recorded by 1590s.
です isnt a verb. If there is a verb, you use the ます version and it makes it polite. In the absence of a verb you use です to be polite. You can omit です without changing the meaning but you will sound rude. Ive read that だ is masculine casual です but i dont know all the stigma with actually using it.
In an audio book course I was listening to before, they explained that だ is simply the informal version of です, and didn't denote it as masculine. Perhaps it's more common for men to use the casual form? You hear it a lot in anime in any case, where they use casual form much more extensively than what is accepted in normal society.
Although it descends from a verb, and it can generally replace a verb in most constructions, it is not considered a true verb because it can be used in certain situations where a verb cannot (particularly after na-adjectives). Also, while it is hard to see because Japanese doesn't have spaces, it is enclitic while other verbs aren't.
あります means "to exist" and wouldn't work here. There is nothing existing in this sentence, just a state being described.
安い is an い adjective, meaning that it already acts as a verb "to be cheap" so 野菜は安い alone is a completely valid structure.
です can also be added here to make it more polite and is required with non-い adjectives in order to complete the "X wa Y desu" "X = Y" sentence structure. Equating two nouns/a noun and adjective together.
If you wanted to say cheap vegetables exist you would have to place the adjective in front of the noun it is describing to link them together
安い野菜があります - "There are cheap vegetables"
This has a different meaning to the one for this question though.