> Wouldn't it be possible to carry the same amount of kinetic energy with lighter ammunition?
Running just on the math, it seems the answer would be "of course":
E_k = 1/2 m \* v ^ 2
Increasing the velocity actually increases energy much faster than increasing the mass (by, say, making bullets out of depleted uranium or tungsten). If you convert a lead (density 11 g/cm^3) bullet into aluminum (2.7 g/cm^3), you need to double the velocity to make up for the 4x loss in mass.
But we're not only concerned with kinetic energy. Momentum also matters. Or, in shooting parlance, "power factor", measured in grains (1/7000th of a pound) x velocity in feet per second. Momentum has a much closer correlation to recoil than kinetic energy. It also affects ballistics - a hypersonic lightweight round will have a different curve than a dense, merely supersonic traditional round.
Other practical concerns are also relevant: lead is an excellent lubricant/bearing material and aluminum oxide being an extremely abrasive cutting material...lead, bronze, cast iron, and other dense metals are more amenable to firing out of an interference fit with a barrel than light metals (of which aluminum is just one example, but a fairly representative one). Lead is highly ductile and mushrooms on impact, but aluminum is brittle and shatters on impact. A round fired at higher velocity spends less time in the barrel, so you need more powder, faster powder, and longer barrels to accelerate it more quickly. And the bullet is not the only thing ejected from the barrel: There's a supersonic jet of propellant gasses that contributes to both recoil and noise.
500 years of (un)natural selection in the field of ammunition materials science has left lead at the top of the charts for a good reason. Most lightweighting efforts have focused on reducing weight in the brass case, which is just packaging and becomes extra mass.
Finally, a combatant worrying about paperwork says something about the one-sided nature of recent wars: Million-dollar soliders applying overwhelming force and unimaginable funds against desperate guerillas. I wonder how quickly the slow-changing military will be able to respond if there's a war between superpowers.