The real question is, what do you imagine that you can do with the .300 Ultra that you can't do with your '06? Sure the Ultra shoots flat, but the best kept secret in the industry is that all modern rifle cartridges shoot flat, between the muzzle and the zero range. Beyond the zero range, all of them drop off sharply, and the Ultra is no exception. With a 200 yard zero, the Ultra's bullet arrives at the target 4" higher than a similar bullet from the '06, but over the subsequent 300 yards, the Ultra bullet drops an additional 40".
If you are looking for a long range target round, the .300 Ultra shines in that it can send heavy for caliber VLDs down range and those slugs won't go trans-sonic until its well past 1500 yards. But that doesn't necessarily make it a better moose rifle than your '06, particularly in an off the shelf, light weight, factory rifle.
I have no problem with folks who prefer to use powerful rifles, provided they can shoot them. I like them myself. I've owned several rifles chambered for large cartridges like the .375 H&H, the .375 Ultra, the .416 Rigby and the .458. I killed my African buffalo with a .500 Nitro, but I don't choose a faster bullet when I think I need to put more power on a game animal, I choose a bigger bullet. When the very fast Ultra bullet arrives on target, its still just a .30 caliber bullet.
If you are serious about long range shooting, the .300 Ultra has much to offer, and might arguably be a better choice than the slightly larger .30-378, but its unlikely going to be able to produce its optimum performance in an inexpensive, light weight, factory rifle. The stock of that rifle will probably fail without bedding and strengthening, heavy recoil will preclude long shot strings, and the rifle might never shoot well enough to inspire its use at long range.