No, crows aren't stupid. They are very cautious and perfectly aware of their surroundings and possible dangers. A couple of crows has been our neighbours for many years; they've known me and my pets for a long time, so they got used to us, and my birds of prey don't set them off. This spring, these crows got bold because they saw me feeding jays and Yoll not giving a damn about it; so now every morning I see a male crow sitting under my windows and waiting for snacks. He picks up Yoll's leftovers first, and once he finishes up, he waits for the treats from me. And I'm totally okay with treating him. That male crow was diligently picking up Yoll's fluff and feathers for their nest this spring too.
A sparrowhawk male came by today and tried to slap Yoll. The crows saw that and slapped that sparrowhawk himself instead, saving Yoll from disgrace in the process!
No, I don't consider crows as vermin. There's just as many of them in the city as the city itself can provide for. Their quantity directly correlates to their food supply. If the crows are gone, their niche will be filled by other omnivores; seagulls, for instance. And no, it's not crows who eradicated all the smaller birds in the city; one should blame city's communal services for cutting down all the bushes and grass, destroying the food chains involved. Crows are feeding on ducklings not because they're vermin, but because there're so many ducks in the city that they're nesting up in places where only the lazy won't try snatching away their offsprings. Additionally, crows at least partially regulate sinanthropic birds' populace by picking up sick pigeons and rodents and cleaning up the carrion, thus preventing diseases from afflicting larger flocks. Crows themselves are herd-controlled by goshawks; there're plenty of those in the cities lately too.
If you're annoyed by crows - for example, if they're too aggressive due to their offsprings leaving nests, then the best way to mitigate this is to remove their nests from the trees before the birds lay eggs there in the early spring. Shooting crows within the city boundaries, much like shooting any wild birds without a proper license, is considered poaching and is against the law. I'm addressing this specifically to those people who'd want to tell me in the comments how much they'd like to "shoot down all those grey rats who snuffed out all the nightingales".