[Sarajevo]

In some places they lay a lot of importance on hand to hand combat, is that really the end all when other aspects are neglected?

Yes

All the other items you mention are only tools to assist in the accomplishment of the mission.

[Red6]

I don't know what your position is from your response, but as an example I would say look at an EIB and what is required to earn this badge: http://www.armystudyguide.com/content/EIB/EIB_Information/eib-stations-points-tasks.shtml

-Prerequisites to test for this badge are:
-Volunteer for EIB testing.
-He must meet the standard prescribed in AR 600-9, The Army Weight Control Program.
-Pass APFT with 70% in each event for his age group.
-Receive the recommendation of the current unit commander. Basically have no unfavorable personnel action (i.e. trouble).
-Qualify expert with the M16 series rifle/M4 carbine day (within last 12 months).
-Score expert on the 11C Gunner’s test, if an 11C MOS.
-Pass land navigation with AN/PSN-11 (PLGR) (day) and night land navigation within six months of testing date.
-Pass EIB standards for the 12-mile foot march within 90 days of testing date.

That is a good example of something that tests “all around” and has some meaning. Some guy that weighs in at 115 pounds and can score 330 points on a PT test if you had an extended scale but can't march with a ruck or is dumb as nails is worthless. The soldier needs to have good all around skills, and PT is just one aspect. Likewise if I have someone that is fantastic in combatives, but is an insubordinate dork that can't get along with his peers nor shoot straight if his life depended on it, is he a great soldier?

My point is simple- Don't emphasize physical fitness to much, it's but one aspect, and probably not even the most important. When it comes to physical fitness or shooting people often get tunnel vision.