Timbo really hits it right on the nail head and sinks it with one blow. But, what is true of the Mosin is also true of the K98k (or other M98 based Mausers), Enfields, you name it. Military rifles are like 4x4 trucks: rugged, reliable, well-built, but not meant for the drag racing track.
There are superbly accurate military rifles. The Finnish M39 was held to among the highest standards of accuracy of any general issue military rifle in WWII. The 91/30 not so much, but they were accurate rifles. The Soviets didn't pick hyper-accurate 91/30's to build their sniper rifles, just rifles off the line. They then fine-tuned them for service as a sniper's rifle. Any military rifle is designed to hit its target. They all will. But in the din of battle, men just were rarely in positions to hit a man between the eyes by design (you know, men move around, duck, all those things to avoid getting hit between the eyes).
But, reality in this case simply is, they were never intended for bench-shooting. They were intended for accurate fire under severe conditions. Neither was any Mauser issued to any military or Enfield. Indeed, the Enfield was savaged by the English shooting elites prior to WWI as pathetic in the accuracy department, so much so that the Ross and P13 were introduced in their respective parts of the empire. The Ross, which was more accurate, was incapable of handling the battlefield. The p13 fired an insanely powerful round (way too much for a combat rifle) and in any case, WWI jumped up to stop its implementation. It was modified as the P14 (and the M1917) and made a great combat rifle, but in no nation was that action actually retained for front-line service after the war.
Now, there are very accurate versions of just about any military action, the Mosin is no different. Indeed, the Mosin shares many of the same characteristics of modern bolt-action rifles., including the Remington 700. Swedish M41's, Finnish sniper rifles up to an including the TKIV 85, various other Mauser snipers (including Springfield), the French F1, all prove that standard military actions can be made into very accurate rifles.