The number of wardens in the places that I hunt varies based on how prevalent poaching and other wildlife crimes are, and the popularity of the area.
Where I will be hunting mule deer with a muzzle loader later this year in Utah, for example, there will be three to four game wardens patrolling an area of about 400 square miles - working together and individually. During the "rifle" hunt, the number will increase to somewhere between eight and fifteen wardens for the same area. (The "rifle" hunt is much more popular.)
However, on the other side of the state and at the opposite end of the spectrum, there is an area covering 7,300 square miles that only has one game warden assigned (and no Forest Service officer - but that's another subject). Where the other wardens only have about 100-130 square miles to cover, each; this guy is responsible for everything going on in an unpopulated area larger than the state of Connecticut or the country of Kuwait. Even though it is much less popular and has much fewer game animals, the massive area still has to be patrolled. By one guy.
Why do we have so many, overall? I think other posters hit that pretty well: Because we do have big problems with poaching, waste of game, and 'wrong take' (shooting a bull elk with a cow tag, shooting a moose with an elk tag, shooting a buck antelope with horns too short to be legal, etc.).
Just yesterday, the Fish and Wildlife dropped a press release asking for information about two bull elk that were shot a couple hundred yards apart and left to rot. Not only is the waste of game a major issue, but it's not rifle season anywhere in the state and that area doesn't have an elk season, at all.
Why so different? (Speaking of the areas that I hunt or have lived.) ...Because a lot of people, especially those living in very rural areas or in the mountains, think they can do - and get away with - whatever they want. Unfortunately for everyone else, more often than not, they're correct. Plenty of people from cities do stupid things, too; but most repeat offenders live out in the boonies, 'where the law don't go' (...until someone turns them in).