The Wikipedia article explains that in the strict sense the last use was in Burma in 1943. Why did shrapnel cease being effective? I understand its limits in a trench war, but surely there was enough movement in WW2 that would make shrapnel useful. Or was it superseded by something else?
Shrapnel shells were replaced with high-explosive shells. This was because high explosive shells were more versatile. Let me explain why.
High explosive shells did not lose lethality with long range and high trajectory as shrapnel shells did (even with a small gunpowder charge to spread the balls in a shrapnel shell, it relied on the velocity of the shell from the gun to be effective).
High explosive shells could be used both in a high trajectory and directly, while shrapnel shells were only effective firing directly or at least with a low trajectory.
Shrapnel shells were really only lethal to the front, as the steel balls spread in a cone forwards, while high explosive shells are effective the whole way around (although ww2 vintage shells, especially lighter ones fired at a lower trajectory tend to deliver most splinters to the sides and a minority to the front and back, see this image).
High explosive shells have better lethality. A 75mm shell will have a 15-20 meter range to the sides and 10-12 meters to the back and front where splinters are deadly to an unprotected enemy. While a 75mm shrapnel shell covers a larger area, roughly 300x25 meters, there will be plenty of room within that area that is not hit by any shrapnel.
High explosive shells are highly effective against field fortifications such as wooden bunkers, trenches, mortar and gun pits and so on, while shrapnel is not. Even in a fluid battle, you will soon encounter enemy troops dug in to some degree, or even just taking cover behind rocks, logs and in ditches and other terrain features.
A high explosive shell can kill, maim, wound or stun an enemy soldier or destroy equipment though the force of the explosive blast even if no splinters hits enemy soldiers or equipment. It can also ruin field fortifications, destroying the cover of the enemy for your upcoming assault, which shrapnel shells cannot.
The bottom line is that the high explosive shell was a better killer, and there was nothing the shrapnel shell could do that the high explosive shell could not, and usually much better.
