We're already testing the next ammo, and it won't be a cartridge as we know it.
What "controversial" issues does the 5.56 have?
Not enough lethality - but frankly, that's not modern warfare. We stepped away from DRT massive lead bullets to small jacketed ones to shoot them more often and get more hits on the battlefield. Since human soldiers and existing terrain are most likely going to stay the same, it's 3-500m max, and recoil less than 35 pounds. That means, small bullets, and dealing with the enemy not shooting back - which isn't Dead Right There instantaneous kills. You can't even get that with the .50BMG, so stop trying.
Not enough cartridge length - so, eliminate the cartridge. Now, it's not a problem.
A sealing chamber that doesn't need an expanded brass case to do it - ok, no brass, allow gas pressure to act as the counterpressure. Like how gas pressure on the piston behind the AR bolt balances the pressure of the case against the face, have the bolt seal by using pressure to do it.
Failure to extract - with no brass case, there's no failure, period.
Failure to feed - which is caused by magazine design. The best magazines aren't complicated high pressure spiral spring powered, curved double stack columns feeding into a straight mag well. What's with that, no wonder the AK is a reliable feeder, and the AR took 40 years to get a magazine that works - the Pmag. So, make it a straight column with clock spring power that exerts the optimum pressure regardless of the number of loads in the stack.
Jams - caused by long cartridges that point too high and then don't chamber, blocking the bolt travel - use a short fat round that doesn't hang up against the gas tube, and is sufficiently tapered to funnel into the chamber. With a shuttle bolt that operates in a vertical plane, it can slope enough on the leading edge to finish pushing a slower round into the chamber.
Not being able to have the optimum bullet shape - pretty much a no brainer now, it isn't held by the case neck, and can be just exactly as long as needed for the 300-500m normal window of infantry combat.
The Army already has enough prototype weapons to run exercises in Battalion strength, and SOCOM is already signed on to help test. Since the brass case is gone, ammo weight 40% less, which means 40% more rounds per pound issued. That's 40% more firepower, and hits go up by the ratio 40% more ammo provides. That's results.
Most of the historically challenged keep reaching back and suggesting a cartridge that already exists, when the track record of adoption is to accept something that didn't exist AT ALL before. Wake up, what we're going to get isn't currently used anywhere or even given a name outside a few test labs. It's named after the program that created it - LSAT.