The tumbling 5.56x45 is no myth. It's a well documented phenomenon that almost all non-expanding spitzer type bullets tumble, or at least reverse, when transiting tissue. The reason is that the center of gravity is behind the center of aerodynamic pressure. When spitzer type non-expanding bullets hit flesh, they are no longer properly stabilized for the medium they are in. They are more stable in a mass forward orientation - just like a dart, and tend to flip over. This is true of the 5.56x45, 7.62x39, 7.62x51 and all other modern military bullets.
What makes the 5.56x45 M855 and M193 unique is the combination of high velocity, thin jacket and deep canneleur cause the round to tend to fracture and break into several pieces when it starts to flip.
ZigZagZeke makes a correct observation, but comes to an entirely wrong conclusion. Because modern low intensity warfare is primarily counter-insurgency operations in urbanized terrain, the basic war fighter formation is the infantry squad, typically on foot or in light vehicles. The weapons at hand are what are normally organic to the squad or fireteam, which means support weapons may be a ways off. In such a case, the rifle must function as general combat weapon, DMR and even light machinegun. It will have to deal with barriers that are typically found in urban areas. Further, body armor will probably increase in use amongst enemy personnel - particularly in the case of well funded insurgents finance with petro-dollars. Soft body armor has already been found in the hands of insurgents.
In the above scenarios, the soldier needs a weapon that can be used for precision fire (to limit collateral damage), counter-sniper operations, suppressive fire and house clearing.
While the 5.56 has performed astonishingly well as an infantry rifle, despite its critic, it does lack penetration and long range capability. This void has been filled by the DMR in 7.62, but this weapon is typically heavy and lacks firepower. Organic machineguns are even more of a problem, and the M249 has proved to be lacking in many respects.
Alternative rounds like the 6mm and 6.5mm intermediate rounds have extended range and penetration over the 5.56 and the 7.62x39, while retaining light weight and controllability under auto-fire. The 6.5 in particular has proven to be ideal for long range shooting.
If one envisions a modular weapon system with a single cartridge, it is easy to fill the roles of rifle, carbine, DMR and LMG with a single base system that is both adaptable and portable. Should heavier firepower be need, that could be provided by vehicle mounted weapon.
For those who advocate the 7.62x39, it has many problems. As noted, it has historically been a notoriously poor stopper. As noted, it tends to go right through a target, doing comparatively little damage. It's really not a well designed round ballistically speaking - but it was an easy transition, since like the German 7.92x33, could be made on existing (modified) machinery.
When paired with the right bullet, the 7.62x39 becomes much more capable - after all, the 6.5 Grendel is just a modified 6MM PPC, which in turn is derived from the 7.62x39.
In the past, the US has always gone into wars with the wrong weapon, designed around the last war Why not design a round that is more widely adaptable, so we don't have top dust off old designs, or create new ones to deal with the new situation.
Finally, and has been mentioned many, many times in this thread, the reality is that there will not be any changes in weapons or ammunition in the near future. What we have now is perceived as 'good enough', and small arms have the lowest priority when it comes to weapon systems. No one makes their career managing a rifle program.
The discussions underway here are really in the range of 'what if'. The ARC trials of the 1980s showed that the Army was not interested in any new small arm system or cartridge unless there were significant advantages - for example, at least a 100% increase in hit probability.