Fremmer, I've pretty much always used my '06 when walking-hunting, doing the cross-country thing. High odds of jumping a buck and having to shoot him on the run. Like you, I've always figured that I could probably cure a bad hit with an '06 easier than with a lesser cartridge.
I've generally been lucky on running deer. I did hit one buck's spine just back of the shoulders, though, and had to use a second shot. Weird deal: When I walked up to him, he was up on his front legs. Made a sort of bellowing or roaring sound, and really threatened me with his horns. Didn't do him any good, of course.
But, just meddling around where I figured more on up close and personal, or just sitting and staring at an area where calm deer and shorter ranges were likely, the .243 works just fine.
"Situational choice", I reckon.
Heck, the last year or two before we lost our old deer lease near Uvalde, I got where I was walking up on sleeping bucks at mid-day. Ten, fifteen yards. Figured I oughta switch to a pistol. The last mule deer I killed, I walked up out of a rocky creek bottom and saw him at maybe 25 or 30 yards. I about halfway apologized to him for using a rifle. Shameful.
Art