At SCI last winter I was chatting with Bill Huber the founder and President of Swift Bullet Co. His perspective is a good one. He said, "Your bullet is the least expensive and most important component of your hunt". The cost fraction that a premium bullet adds to a Safari is minimal.
This past July in Limpopo, I took two rifles for the trip. A lovely little FN Browning Hi-Power Medallion grade in 308 Win which I loaded with Federal Fusion, heavy for caliber 180g bonded bullets. These are hardly "Premium" but do feature a bonded lead-core bullet that has a great reputation for massive, reliable expansion of 2.5-2.7x at normal hunting ranges. I did not use A-Frames because the 180g ones simply failed to group well with my old rifle. Same was true of the Federal Premium Terminal Accent ammo or some of the others like Barnes TTSX. I could have dropped down to a shorter, lighter projectile but since the 180g Fusions shot great for me out to 300y, and since I was only planning on using it on the smaller critters, I figured it would be fine. Boy was I wrong about that!
They were not fine, they were like shooting with Thor's Hammer! I ended up taking five animals from Duiker to Gemsbok at ranges from 20y to 202y and ALL of them dropped with one shot. All of the shots were total pass-thru and the furthest any ran was 60y. If you have ever had the experience of shooting a valuable game animal and having it run off as if nothing happened and have the PH tell you that you "Missed" or that was not a good shot and then find blood and know that you screwed the pooch and let down yourself and the PH, you know why you want to do everything possible to avoid that situation. A few extra bucks for premium bullets is a small price to pay to insure a successful hunt.
The 2nd rifle I took was another lovely big FN Browning Hi-Power Safari Grade in 375HH. It was loaded with Barnes TSX 300g copper bullets. My rifle shot them well and I have a lifetime supply of them. The plan was to use these on the larger Zebra, Gemsbok, etc as practice for a future Cape Buffalo hunt. The 308 was working so well that my PH dissuaded me from using the larger magnum except when we went out for Wildebeest. I took a nice Blue Wildebeest at 160y with the 375HH. The TSX did what it should and I have no complaints.
Final thoughts. On the last day of hunting on my Limpopo Safari, my PH and I sat on a mountaintop overseeing a pan to the South. The fine sense of contentment from having made every shot count and cleanly and efficiently taking each animal and performing well as a hunter (even though limping from a tweaked ankle all week), was one that stuck with me for weeks following my trip home. It was so satisfying and peaceful, that I would never want to spoil that by a botched shot that wounded an animal, leading to the loss of such or a lengthy tracking job that could have been avoided. I have experienced both and I can say without question the satisfaction of the former is far and away better than the utter despair of the later.
I put a lot of time, expense and effort into my hunt preparation. It is part of the fun of the project but it is also insurance for making sure that at the end of the hunt, I go home with that deep satisfaction of a job well done. Short answer is "YES", take the premium bullet that shoots the best in your rifle. The bullet placement is more important than the actual bullet but once it hits where it should, having the ability to penetrate reliably, even thru bone and finish the job with the least pain and anguish is absolutely the #2 priority.
I once asked my PH why it was necessary to get out and stalk so close to an animal as opposed to setting up on a hill and shooting from 400y, 500y or longer with a precision rifle? His reply was clear, concise and to the point. He said, "We do not fool around with longer shots in most cases because we are better hunters than that." Nuf Said.
Stalk slowly and quietly, get in close, aim fast but shoot slow and hit your target confidently and you will have a great hunt.