Yes, I agree with you completely- people should do research before taking on a new animal-and it's not the type of pet, it's the type of person.
I believe the reason the majority of cities ban urban hens is due to potential safety hazards and nuisances though- smell, increase pest attraction, chances for salmonella, objection to backyard slaughter, noise, etc. etc. Overrun shelters is likely not much of concern for many cities (b/c government shelters are rarely no-kill, so just euthanize "excess" animals).
It seems the overpopulation problem is more of an issue that's concerning nonprofit organization shelters and sanctuaries. It would be absolutely great if everyone kept their hens forever, but a good percentage of people don't. Even in cities where it's perfectly legal and a ban isn't to blame (like my city for example), abandonment rates are still extremely high. I've heard of sanctuaries whose chicken abandonment rate has increased by 500% percent over the last decade! Their chicken rescues were once only due to cockfighting, but now are due overwhelmingly to urban farming.
And then, even with responsible owners, there is still the case of the roosters. Many chicks end up being roosters and people can't keep them in cities for obvious reasons and don't know what to do with them. So they abandoned the animals to us. We have far more roosters than hens! This is also one major difference b/w other pets. Imagine if no one knew the sex of their puppy until 6 months, and that every male (which would be half of all puppies) immediately must be killed or sent to shelters? Think how much higher the abandonment rate would be then, yikes!