The 7.62 X 39 used in the AK 47 is almost identical ballistically speaking to the 30-30. Although the AK is reputed to be inaccurate, I have fired several private, clean, tight AKs at 200 yards, and they are semi-reasonable for a military rifle, that is you can easily hit a square foot target somewhere. They are also reputed to be impervious to dirt and function well with '0' maintenance/abuse in Third World hands.
Army blurbs claim that the 5.56 with a the newer 70 grain bullet is killing people at 5-600 yards with excellent accuracy. But there's a problem. Seems to be that if you miss the kill shot, the wounds can be sustainable and the bad guys keep shooting. If they are behind even minimal cover, the bad guys are pretty safe, especially at longer ranges. That's in the open. In any kind of vegetation, the 5.56 is easily deflected and the M16-M4 series is indeed a bear to keep clean and yes, it is still reported jamming when most needed. And yes, troopers do buy and mount aftermarket parts to improve reliability.
Tests are underway with 6.5 and 6.8 ammo, with very impressive results. BTW, seems Army marksmanship has improved 1000% since the spray and pray tactics of Vietnam. In regard to "light weight:" by the time the Army finished modifying the original M16 to the point where it would sort of work most of the time, its weight difference with an M14 became less obvious. The big weight saving was due to the 5.56's much lighter weight, so a soldier can carry many more rounds. Also, there's no more "spray." Three round burst on auto.
We have more than enough operational data to support everything that you've said and more. The problem is, that the system we have in today's DoD isn't interested in the best possible equipment for the troops - just maintaining their jobs and LOOKING like they're doing something. Most of all, the long-term GS managers have emotional investment in "their projects" and fight tooth and nail to prevent anything to replace them. And industry is just interested in making money with the big-buck (and largely useless) projects. Ammunition is a big deal because it is expensive in the volumes needed for training and combat and because we have massive stockpiles of existing stuff they want to keep using. Similar to the near-fielding of the superior .276 Pederson cartridge in the 1930s (which would have given the Garand a 10-round capacity) that was blocked by the army Chief of Staff, Douglas MacArthur because of all the costs of replacing .30-06 stockpiles.
As we get further down the "all-volunteer" road and the people who serve in the armed forces are just "somebody else's children", don't expect any greater efforts to find and field better weapons. They don't care.