I am not sure about this, and I suggest there is a lot of greener on the other side of the fence. My views on America are from good friends, colleagues, clients and business, together with reading and huge of American hunting literature and follow the likes of Randy Newberg, Craig Boddington, etc on YouTube. I have not been to the US. But what is clear to me is the US is a collection of very different states developed by peoples of very different backgrounds and cultures, with many of those original cultures still very close to the surface.
I have though lived and worked in parts of Africa threat of violence from gangsters armed with AKs and Pangas is high and slept with a loaded shotgun next to my bed for this reason. I was going to make my life in Africa, but have now spent the majority of my life in Scotland.
Weapons of war vs Sporting guns. I have little interest in the former, but a huge interest in the latter. I can appreciate the engineering and inventiveness of the likes Henry, Mauser, Browning, Luger, Maxim etc etc but don’t feel the need to possess an FN FAL or a Glock, nor do I feel aggrieved that I am unable to freely walk down Princess Street in Edinburgh with a fully loaded AR waving my 2nd Amendment rights like a MAGA supporter.
I quite like living in a society where the Police are not routinely armed and if I have a minor road accident its very likely I will be threatened with a firearm with the other driver being terrified that I might be about to threaten him.
Coming back to hunting. The US can thank Theodore Roosevelt. He was a hunter and who loved wild spaces. It was him who really laid the foundations politically the wide access to wild lands that the Americans now enjoy. It may have been that many species in the US went from huge abundance to extinction (or at least extinct in most of their former range) in a very short space of time - 10 to 20 years to wipe out Buffalo and Elk herds in most of the US. Wildfowl and pigeons were shot in vast numbers by market hunters.
In the US hunting seems to be very much part of the culture, and thanks to the US Fish and Wildlife, and State game departments, there are now thriving game populations across most of the country, and through a controlled tag system hunters of comparatively modest means can get a tag or two and go on their own adventure and take a deer or two for their own consumption. And ditto with wildfowl etc. Private land has different levels of access and very much depends on where you are.
In the UK we have limited public access for hunting. It really only exists below the high tide mark on the foreshore after wildfowl. But even this has been severely restricted. Up here for £25 I can get a wildfowling permit for a large area of foreshore and I am free to go and lie in the mud after duck and geese. No bag limit per se - nature takes care of that.
Just about all the land in the UK is privately owned or managed. There is common land in many parts, but this jointly managed / owned by commoners. Forestry Scotland is owned and managed by the Scottish Ministers.
So for deer stalker there are really only two choices:
1) you go all in - stalking takes over your life and you fully commit to managing quite large areas, or pay lots of money to do so. Number of deer you “have to” shoot is measured in the tens if not hundreds per year. For most of us, such all in is pretty much impossible thanks to careers, families and other interests / obligations.
2) you take the odd day of guided stalking. Typically you pay a few hundred pounds to follow somebody else around the countryside on their “permission” or “estate” and shoot what they tell you to. Some guides and estates are very good others are not.
Or you shoot game birds as part of a shoot or syndicate.
What we don’t have in the UK, which you do have in the US and mainland Europe are the accessible means for younger and less well off hunters to be able to spend a few days a year in the woods, mountains etc and taking one or two birds for their own consumption.
There is a constant concern that youngsters are not coming into stalking and shooting. For anybody with a family, demanding job and a mortgage or rent to pay most hunting activities have to take a back seat, whereas I think in the US going out hunting is more part of life - you go off to the mountains with a tent, your kids, a rifle and fishing rods and you have fun having first picked up a deer tag and fishing permit.