When I first came into the Army we had a 5 event fitness test which included: the
Overhead Ladder;
Inverted Crawl (kind of a crab walk forwards and backwards); the "
Run Dodge and Jump "(a mini obstacle course in which you ran around obstacles and jumped over a trench;
Situps; &
Two mile run (in fatigues and boots). It was a really good test from the standpoint of measuring functional strength, but it was time intensive to administer, and it was really hard to train for. The overhead ladder was a combination of strength - with technique, and the only way to be good at it was to practice it, That meant ladders everywhere- shower rooms, hallways, outside. And as a friend reminded me- most of them were rusty and your hands were like hamburger at the end of doing a set

(and as a stumpy guy- no matter how much I practiced, I was never going to max the perverted crawl no matter what I did!)
When they went to the current APFT- (which I think was in 1980 or 1981)- much of the rationale was exactly what Davejean90 lists above- availability of time and equipment to administer. We'll see if this new test really gets implemented- every month for the last 30 years the Army Times has been discussing a new PT test- and the current 3 event test is still here. I think that frequently they confuse the test with how they should be conducting strength and fitness training. The APFT is probably just fine as a snap shot of personal fitness- but it is not what PT should be about, which should be about building strength, endurance and cardio for the tasks required for your MOS.