Would you guys really want to take down a large grizz or brown at a distance with a 30-06? The poster seems he will not be with a guide if he is living up there. I would be comfortable with the 30-06 with heavy for caliber bullets in a defensive situation ... you are only going to get off one shot and it better be on the money. The poster is talking about a hunt situation of up to 500 yards, IMO would want something like a 375 H&H. I would not want to be the one bushwhacking for an injured bear.
You ask a good question - would I
WANT to go hunt grizzly and brown bear with a .30-06 Springfield? Hmmm...I think I take it more from the perspective of COULD a person safely and reasonably do so and the answer is yes. With quality, deep penetrating bullets (Barnes? Partitions? Trophy Bonded?) with a high sectional density, the ought six will get the job done.
If I was in the possession of that gun and the chance to go on a hunt came up, I wouldn't feel compelled to run down to the store and buy something else. I won't be alone on the hunt, I'll have partners. And shot placement and penetration are still "key" regardless. Bear (ha!) in mind that the OP did state that recoil was an issue that concerned him. That being the case, COULD his .30-06 work? Yes, it could. While it might not be the
first choice (bigger is better when the game being pursued can, and will, kill you) it is not a ridiculous choice either. Many a big bear has been killed with less.
Heck, if I had to chose between hunting a big bear with a .338 Win Mag shooting 'cup & core' bullets or a .30-06 shooting a heavy Barnes TTSX or Partition, I think I'd take the better BULLET option over the MORE POWER option. Yet, people back in the day got it done with cup and core bullets time and time again. We have it so much better now.
Having said all that, I have a .338 Win Mag in the safe right now and faced with a bear hunt, I'd absolutely pull it out for the job. But more because I already own it and can shoot it (mercury recoil reducer in the buttstock and Limbsaver on the end of it.) It still wallops me when the 'fun lever' is pulled, but my Remington Titanium .308 has more painful recoil to me (the velocity of that LIGHT gun coming back into my shoulder is just vicious.)
As for the 500 yard thing, I think the idea of bears and long range shooting got 'merged' a bit. He wasn't thinking of shooting a BEAR at 500 yards. He wanted a cartridge for Alaska hunting that was capable of a 500 yard shot. (Caribou? Sheep? Mountain Goat?) But the way his first post was written, it came out sounding as if he wanted to take a 500 yard shot at BEARS and he clarified that wasn't his intention in a later post.
Now, if I decided I was going to make it my life's mission to hunt bears all the time, then I think one would be prudent to GO BIG and for me that would be a .375 H&H. It'd have to be heavy, too, because I'd need to be able to shoot it without flinching. That would mean I'd have to work out more to get my skinny little 'city arms' in shape to carry something weighing 11 or 12 lbs around all day, ha! Still far lighter than the 23 pound M-60 I had to 'hump' around for Uncle Sam, so there's that...