Someone asking this question is likely new to long-range shooting. The key to making long-range hits-- on targets or game -- is shooter skill. Shooter skill is developed by consistent and voluminous practice. Practice is made possibly by affordable ammo and a shootable cartridge (ie, low recoil).
Many factory rifles these days are capable of 1 MOA accuracy with some ammunition. Thus, mechanical accuracy of the rifle is rarely the issue. Often an inadequate sighting system is used, or the shooter does have enough practice to take advantage of what even a moderately LR-capable cartridge can offer.
A magnum cartridge is often a poor starting long-range cartridge because the ammunition is expensive and the rifle has recoil such that it is very easy to develop bad habits. 308 is not the best long-range cartridge, nor is it the best match cartridge (as you said), but it is a good starting cartridge because recoil is low, factory ammunition is available for both hunting and "match" almost everywhere, and it is reasonably competent at medium ranges (say 300-700 yards). It is effective on game further than the vast majority of shooters can shoot it precisely.
-z