jamesinalaska, I am no hunter, so I will leave it to those with experience hunting with these rounds to share their first-hand knowlegdge. But I will point out that the argument you put forward could just as well be used to say that everyone should be hunting deer with .50 BMG.
The actual numbers say that that a hot .357 round from a rifle leaves the barrel with a little more than half the energy of a typical .30-30 load, a hot .44 Special or .45 Colt at about 3/4 the energy, and a .44 Magnum pretty darn close ot the .30-30 at the muzzle. These are some numbers from
http://www.chuckhawks.com/rifle_ballistics_table2.htm with the first number in fps and the second in ft-lb.
Cartridge (Wb + type) V/E @ Muzzle V/E @ 100 yds
.30-30 Win. (150 FP) 2390/1902 2018/1356
.30-30 Win. (170 FP) 2200/1827 1895/1353
.357 Mag. (158 Sp) 1830/1175 1427/715
.44 Rem. Mag. (240 FP) 1760/1650 1380/1015
.44 Rem. Mag. (275 HP) 1580/1524 1293/1020
Clearly the .357 is the weakest of the bunch, but when you compare these numbers to handgun ballistics you find that the estimated power of that .357 at 50 yards (say 900-950 ft-lb) is still substantially more than any factory .357 load generates from a handgun at the muzzle, ever.
Unless you really think that a hot .357 load from a revolver at point blank range wouldn't be enough to put down Bambi humanely, then, at the "longest possible shot is 75 yards, much more likely is 20-50" described by the OP, .357 seems like more than enough if the hunter does his part.