I don't know what the case is in NE US, but in my town in British Columbia, the deer population is out of control in the metropolitan area, and every time a cull is mentioned, animal rights activists put a stop to it through loud and effective lobbying. It's quite irritating.
The grizzly, as a top predator, was not really very afraid of humans and many people were killed by them in California before they were hunted to extinction. I would definitely not want them around as a farmer in the 1800's. With antibiotics, helicopter transport, and ER rooms today, I might support a reintroduction of grizzlies to the state. There is one on the state flag, after all, and are amazing creatures. On the other hand, I like how relaxed I can be hiking in the California Sierra without them. Hiking and camping in the Canadian Rockies feels a lot different.
Mountain lions (at least the ones evolved when we hunted them for the last 12,000 years) are much less hazardous to humans than grizzlies or wolf packs.
We have an urban coyote population in Vancouver. It's very strange seeing a coyote in the city. I was 20 feet away, once. They are amazingly beautiful creatures.
Even if they were allowed to hunt deer, it probably wouldn't help. So much of the land deer graze over in the Midwest is suburban and have laws in place regarding setting off a firearm.
This limits hunting to public lands, of which, there might be 2-3 within an hour drive of the city. So no matter how much the hunters kill, they aren't likely to effect the populations in the surrounding suburbs.
There are more hunting spots in the rural areas, but those areas are also populated by natural hunters, like wild dogs and large cats.
You can still bowhunt, or at least you ought to be able to...
It makes me very sad to go south and see the huge numbers of roadkills on the side of the highway. Where I'm from, we try real hard to inflate the deer population, since the winters and the coydogs keep the population down so much that the hunting isn't real easy.
This problem is widespread in the urban areas of my rural, pro-firearms home state. They solved it by hiring sharpshooters to kill the deer with rifles at night within city limits. It worked really well and they gave a ton of meat to the food bank.
Which state is this? I'm surprised anyone would authorize hunting in an urban environment at all, given the risk of collateral damage. Just because you've shot the deer precisely doesn't guarantee the bullet isn't going to fully penetrate and keep on going.
Where are these animal rights activists? I'm from PA, the state with more deer than any other, where the white-tailed deer is the official state animal, and I've never seen anyone shed a single tear over a deer hunt.
It's not a simple solution, because it's not very effective. In areas with limited open space, hunting is very much an exclusionary activity. In Staten Island, the NYC Parks Department is performing an experiment in deer sterilization: https://www.nytimes.com/2017/09/22/nyregion/deer-vasectomies...
In NJ there's a restriction from hunting within 450 feet of a building. In Idaho that's probably laughable, but here it leaves a lot of space where you can't discharge any weapons.
There's a parallel with the charge that the "Drug Free School Zone" laws discriminate against minority communities because everywhere you go in cities, you're within 1000 feet of a school.
The hunting restrictions are basically why the deer population recovered to the absurd levels they have. They need some tuning the other way, maybe extend the season (eg, shorten the exclusive bow-hunting season and lengthen the regular hunting season).
If you're not allowing hunting on your property, it would also be good (albeit expensive) to fence it, so deer cannot easily move through, to reduce their available forage.
Wolves kept the deer population in check for eons before humans ever showed up. The real reason the deer population is out of control is because we've extirpated their natural predator. Unfortunately for the forest's sake, it will never be politically tenable to have wild wolves roaming the exurbs of New England.
Mentioned it above but I live in the northern Idaho region. We've grown our wolf population for awhile. Now we are at the point of having too many wolves that we are opening hunting to them.