I own five Smith N Frames, three are .357 magnums; therefore, you can imagine that I believe these are outstanding revolvers.
With this said – and assuming, as indicated in your post, that “shot placement is not an issue” – I would feel comfortable going after mid-size game (whitetails, etc.) with appropriate loads (for example, Federal 190 grain CastCore), with 50 yards being my PERSONAL outside-limitation. I would not hunt larger game at reduced distances, because I believe hunting demands a fast kill and an immediate harvesting of the game; I am afraid that larger mammals might not be quickly killed with a .357 magnum, given my good (sometimes excellent) but not superb marksmanship.
I also wish to add a final thought: with precision accuracy, an appropriate .357 magnum round can probably quickly kill most North American game (obvious exceptions include brown, grizzly and Kodiak bears). However, the certainty of that “precision accuracy” is the key issue. Accordingly, I would opt for several larger/more-powerful revolver calibers, such as the .44 magnum, the .45 Colt, etc.