The modern form of sushi (edomae nigirizushi) is basically fast food made out of freshly caught fish, so you make it and serve it the same as any other street-vended food based on raw fresh meat. The carts also had a covering on them - nobody left their fish out in the hot sun.

Also, real wasabi acts as an antimicrobial agent, which is a historical precedent for modern sushi chefs pre-applying the proper amount of wasabi to each piece before giving it to you.

The taste does change after it's been prepared. They're being a little bit "soup nazi" with the whole counting of seconds bit, but it is better to taste it freshly made.

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It actually makes zero sense to wash the sushi down immediately with sake as it changes the flavor of what you're eating, not to mention the varying flavors and mouthfeels of both sushi and sake. If you have to drink something, make it water - but don't drink a lot before or during the meal or you'll get too full to finish all the sushi.

Sake is considered a rice dish in Japan, and sushi (in this article) is nigiri and not sashimi, so sake would be like an extra rice dish, which is atypical for Japan. I don't see why you couldn't drink sake at a street stall, though, if in America you can drink liquor out of a brown paper bag.