I guess it's a different 'mentality' here in the UK, I'm not saying we have the right mentality as I actually like the idea of bag limits. Over here no landowner wants rabbits on their farm or pigeons on their crops, as such total eradication if that were possible would be welcome on most farms. It's the hunters that try to preserve quarry numbers, but if I am to be honest I'm a little old school or so it seems. Many 'new' guys just seem to want to make a mess of an animal, shoot as many as possible and move on to the next.
Pigeons: We have a few, Woodpigeon (Legally a pest species but regarded by hunters as an exceptional sporting bird), Feral Pigeons regraded as 'fly' rats as well , Rock Doves (look a bit like Woodpigeons but are protected), Collard doves (introduced in the 1950's and have spread like wildfire to become another pest species, taste good as well!) and ornamental doves etc.
Pheasants: Much the same over here, it's a rich man's sport. To buy a young poult it will cost you $3 (most shoots will put 2000 to 3000 birds on the ground), you then have to look after the birds, feeding them and keeping the birds in 'pen' until the birds are ready to be released which all cost money. Total cost per bird from poult to being shot is around $27. The bird is worth $5 at market, so it cost the shoot owners $22 more than the bird is worth to take it from young to shoot able if that makes sense.
Okay, the shoots will charge a gun $45 to shoot each bird, the gun could go down the market and buy a bird saving $40.
The worst thing of all is if we have bad weather, what happens then is that the shoots can not operate at the beginning of the open season, obviously the birds have cost $1000's, so they will hold cheap shoots at the end of the season to recuperate their money. Problem is that there isn't a big market in the UK for Pheasant after Xmas, so a great number of birds are shot and simply buried. That's what happens when things are run as a business.