Done quite a bit of hunting with the 44 mag, mostly in handguns. A 300 grn bullet at 1800 fps is about the equivalent of a modern 300 grain 45/70 load, with a little better bullet sectional density and probably B.C. to boot. With a solid broadside chest hit, sure it will take down an elk, even at 200 yards.
Problem is, it is not always prudent to stretch a cartridges performance envelope in hunting conditions. Will you have a solid rest available?, avoid raking shots?, have time to use a range finder? have the ability to accurately adjust for elevation and windage?, and has that load actually been tested at the ranges you note for accuracy and bullet drop?. If so, then, yes, its a viable choice. But once we start getting out of woods ranges, and traditional black powder / handgun cartridge type situations, most hunters want the power and flat shooting abilities of the usual big game centerfire rifle rounds to help eliminate some of the variables I mentioned above.
Larry