re: It depends........
The answer to your question is that the effective range of the .22 LR round in the harvest of small game is going to depend on things like environmental factors, the accuracy of the rifle, and the ability of the shooter to accurately estimate range in the field and compensate for it.
I do some rabbit hunting with .22 LR rifles. In most of the areas where I engage in that activity in Southern California, there isn't any need to worry about "effective range" as most of the shots that I am presented with are under 50 yards anyhow, and the vast majority of those aren't a longer poke than about 25 to 30 yards.
But up in the high desert country of Modoc County, it's a different matter. There are a couple of places I go to up there where I can lay out prone on a flat-topped rock and snipe bunnies out to 75-100 yards. Doing that, though, requires some skill in doping the wind and accurately judging distance. In other words, it's pretty dang challenging. It's not impossible if you train for it in your practice regimine, but it ain't easy, either.
And it's no place for a tool that isn't up to the job to begin with. So my bone-stock (well, okay, not bone stock, since I replaced the nearly worn-out blued barrel with a stock stainless one) Ruger 10-22 stays in the Jeep (well, okay, it actually stays at home, unless my wife comes with me, since my wife seems to think it's her rifle now). My bolt action CZ 452-2E gets the nod when I've got to push the envelope of .22LR field shooting performance. Missing with that rifle is caused by one thing: the nut behind the trigger, which is me.
Most of the time, I don't need or want to eat a cottontail bad enough to risk gut-shooting one first before killing it clean, so for me, I'd say that the effective range of my .22LR rifle in my hands is about 75 yards or so on a fairly calm and windless day. But since it isn't often windless where I hunt, it's probably more like 50 yards or so.
Like I said, it all depends.........