The vast majority of older military M16A1's are 1:12 twist. This was compatible (perhaps somewhat marginally) with the M193 55gr ball ammo in use at the time.
M16A2's through current M16A4's have 1:7 twist, as do derivatives such as the M4 and SPR.
The twist rate does not markedly increase ballistic range. The increased twist rate came about because of the introduction of the standardized NATO-spec M855 62gr cartridge (using the SS109 "penetrator" projectile with a hardened steel core) and the correlated development of the M249 SAW (aka FN Mini-Mi). Once the M249 SAW was introduced into the field, ammunition standardization meant that all 5.56mm weapons would use the same ammo. The M855 has better penetration of light armor at longer ranges than the M193 it replaced. The now-unused M193 cartridge, however, has better penetration at shorter ranges due to the higher muzzle velocity.
This was and is not a factor in caliber nor twist selection.
The primary wounding mechanism of high velocity 5.56mm projectiles is yaw, dislocation/fragmentation at the cannelure (the ridged circumferential ring where the projectile is seated to the case), and a resultant large wound cavity due to multiple fragments and hydrostatic pressure. In general, with 5.56mm if there is in fact an exit wound it is indicative of poor projectile performance.
Gun store counter stories.
You mean "ball powder". All military cartridges use ball (FMJ) projectiles, excluding some special types (specifically OTM) that are used strictly for long range sniping applications. Look at the side of a 840 round 5.56mm ammo can: "AMMUNITION, BALL, 5.56mm M855". Gunpowder is available in ball and stick geometry, and it was the ball gunpowder that cause initial M16 teething problems.
Despite all this, the basic AR15/M16 design has not changed in 50 years, and the majority of the world's special operations forces use a derivative.
The issue is not expending the entire magazine, it is maintaining accuracy for the duration. Full auto is used for suppressive fire, and generally not aimed fire such as with semi-auto and 3 round burst.
