I'll probably get flamed for this, but I've loaded and shot 125 gr. Sierras in both the '06 and .308 for PA whitetail for years. It was mainly for my father who complained about the recoil from the '06. I built him a nice Rem. 700 in 308 and continued to use the 125's. He killed several deer with that combo over the years, and never had anything even come close to getting away. I'm fully aware that the SD is not what most folks feel is necessary for deer, but both guns shot the 125's nicely, and he shot that 308 very well. His longest shot was a decent 7-pt. at a little over 200 yds. Dropped like a rock.
I know your question pertained to the 30-06, but given the weight/caliber scenario, I think you can see my point here. Some may argue that this weight bullet isn't structured sufficiently to work on deer. Would I recommend it highly ass a great deer bullet in that gun? Probably not. But in the set of circumstances it was used in for Dad, it worked well. The deer couldn't tell the difference. In fact, most of them hardly ever moved...........