Many years ago when I started hunting elk and my only centerfire rifle was a .30-06, I killed a few elk with 150 gr Hornady spire point bullets, then quite a few more with 180 gr Sierra GameKing bullets.
When I upgraded to .300 Win velocities, I switched to 180 gr Nosler Partitions and killed a pile of elk with them. Most of those bullets would shed the lead from the front portion and the remaining bullet would be found just under the skin on the off side.
A few years ago I built a .300 Weatherby for my primary elk rifle. I have killed two bulls so far with it. The first was with a 168 gr Barnes TSX bullet. It went in just behind his shoulder and exited just behind his other shoulder. He turned, took 3 steps, and fell dead. There was 10' of blood spray on the snow on both sides of him.
This past season, I used a 168 gr Barnes TTSX bullet. I didn't wait for him to turn broadside and I foolishly shot him in the center of the nearest shoulder. The TTSX bullet broke his shoulder blade in two at its narrowest part, went through a rib going into the chest cavity, through another rib exiting the cavity, and stopped just under the hide of the off side. The bull dropped dead in his tracks, but his shoulder and the near ribcage were terribly bloodshot and too much meat was lost. The recovered bullet was a perfect Barnes mushroom and weighed 167 grains. The only thing that bullet lost was its blue plastic tip.
At .30-06 velocities, I think any 180 grain hunting bullet will sufficiently reach the vitals of an elk for a killing shot when it is hit behind the shoulder. Premium bullets should hold together better if they hit bone, and they may penetrate deeper on less than perfect broadside hits. Premium bullets should also hold together at higher than .30-06 velocities.
Both the Barnes TSX and TTSX bullets are essentially hollow point bullets. The nose cavity opening of the TTSX bullet is larger in diameter but is filled with a pointed plastic tip for a higher ballistic coeffecient. When a TTSX bullet hits an animal, the plastic tip shatters and the large nose cavity opening promotes rapid expansion, especially at lower velocities.
As for the increased cost of premium bullets, reguardless of the brand of bullets, the cost of that bullet is less than one gallon of fuel that you burn getting to your hunting area.