why is the most revered Jewish food so often fermented?
In addition to the fact that the ancient Israelites rubbed their newborns with salt to 'preserve' their health, I would posit four general reasons:
(1) Living fermented food is best for people on the move. Like matzah, made for folks that were making haste, fermented food lets you bring your live & healthy culture with you. Since the destruction of the second temple, Jews have been spiritually migratory & thus have had to invent an equally transient culture that holds up to different environs. Being book-based (vs temple-based) I think is just as important as having food 'cultures' that you can bring with you, cultures that are alive and can exist in transit.
(2) Jewish food is all about making the most of poor ingredients: cheap & abundant cabbage become kraut, copious cucumbers become pickles, cheap beets become borscht & kvass (Jewish kombucha!), less than stellar cuts of tough meat from the chest or breast become corned beef, and of course grain become deliciously fermented bagels & challah.
(3) Ashkenazi food is about preserving food for the year. And the oldest form of preservation? Fermentation.
Jewish food & fermentation
And lastly (4) because Jews love fermented food the most! Why else would Jews give up - of all things - leavened food (read as: fermented) on Passover? During this holiday, Jews reist chametz, a word derived from the common Semitic rootḤ-M-Ṣ, relating to bread, leavening, and baking. Chametz is also cognate to theAramaic חמע, "to ferment, leaven" and the Arabic حمض ḥamuḍa, "to be sour", "to become acidic". This implies fermented, sour, acidic food!