Shakky, I can give you all sorts of reasons to get a hunting rifle chambered in the venerable 8x57 Mauser. The first and most important is that with decent ammo, such as RWS, Norma and Privi it is a very capable cartridge and available in several useful bullet weights. IMHO, you should reload for this cartridge though.
All of the major North American bullet manufacturers make a decent selection of good bullets.
As far as the bore diameters, I have only run into one with a .318 bore and that was on a Gew88.
There is no reason why you shouldn't be able to load to the same pressures that the axis nations did. 98 actions are commonly converted to cartridges generating as much as 55,000+ CUP. They are strong.
Remington made the 700 in their Classic model in 8x57 that would even be safe at higher pressures although finding cases for those might be another story. Privi seem to have heavy sidewalls so it's a good place to start. Zastava also made the 798 for Remington in 8x57 as well as under their own banner. The rifles from Tradex that I have seen are decent but just keep in mind they are well used and drilled and tapped for side mount bases in some instances.
I have used the 8x57 on Moose and Black Bears as well as Deer. I never recovered a bullet. All passed through with good expansion even at 300+ yards.
I also had a Winchester Model 70 push feed that was rebarreled to 8mm-06. Something I just had to get out of my craw. In all honesty, there was hardly any difference in performance on game or velocities before pressure signs started to show up. It is an excellent combination though and really does show substantial improvement with 196 grain bullets. The biggest drawback is finding barrels in this diameter that are cost effective. The barrel I used came out of Sweden and I found it at a gun show in the form of a blank at a reasonable price. The vendor had no idea who made the barrel and the only marks on the end were the stamps indicating diameter and Sweden.
It's your desire to follow or not. Personally I feel that if you want something different with a power potential between the 30-06 and 338-06 the 8mm-06 is a good way to go. The 8x57 is used all over the world and there were likely more of them used than any other cartridge including the 30-06 at one time. Now, things have likely changed.
At the very least, with proper loads you will not be under gunned for any game in North America.