As with any other firearm it is all about shot placement and reasonable range. The 17HMR will in fact do some pretty amazing things even on larger game with perfect shot placement at reasonable ranges and by not mismatching it against the extremes (like a bear - give me a break). Yes we did kill many mule deer on the ranch I grew up on with 22LR rifles kept on every ranch vehicle from very close ranges... but just like it was in the 50's big game is a luck shot at best with any rimfire.
Like Keith I too had a huge run in with an RFC Mod over his boasting on using the 17HMR as his primary coyote gun so soon after the cartridge was first released by Hornady. He not only could not have had much experience with it in the field yet, but he made claims I knew from much longer (than him) personal experience with the 17 HMR that what he claimed it was just not capable of reliably (you see, I did some of the early field testing of the 17HMR on flesh for Bullberry/Hornady long before the cartridge was released for sale to the general public - hence having maybe the first privately owned 17HMR). So wild claims aside, only you based on your own personal experience and personal abilities can make the decision whether each individual situation on any game animal will allow the fast, clean kill that even a lowly varmint or predator deserves, let alone bigger game no matter what firearm you are using IMO.
I have 3 highly customized and so extremely accurate 17HMR's and their primary use in my hands is for varmint hunting, especially ground squirrels and jack rabbits (although my 3 17HM2's have replaced them to some extent for the squirrels). Even though they are certainly not my first choice for even the larger predators, let alone bigger game, they have handled those larger predators just fine for me WHEN I had no other firearm in tow AND when I only took well placed shots I was very confident I could make and at ranges past experience had proved to me the cartridge was capable of on that size animal. That includes one-shot kills on a few coyotes out to the longest at about 180 yards and a huge bobcat at 80-85. My mainstays, the ground squirrels have been taken well out past 300 yards and jack rabbits to at least 200. Yes I have had some "crawler" squirrels and rabbits, mostly from trying to push the shots too far out or making a poor shot that required follow ups to humanely kill. But all of the predators dropped in their tracks. These are lasered ranges, not wild boasting, and from my own personal experience with the 17 Hummer and 10's of thousands of rounds of them shot in the killing fields. So take or leave them as you wish, but they are fact and not heresay (most witnessed).
Again, only you can decide what your firearm and personal abilities with it can reliably do, so only you can make that all important decision in each situation whether to take the shot or give a free pass. I have given dozens of free passes on borderline shots for every one I actually took with all of my firearms over the years. Wounded game given up on by the shooter to die a slow death is just not acceptable to me no matter what species it is - period.
Best choice is to use the 17 rimfires for what they were designed for and use more gun for anything larger.
L.