Having been the secretary and an elder for several years, I began to realize why time was collected. It had nothing to do with scriptures. Notice these:
Acts 1:15 (NWT) - 15 Now during these days Peter rose up in the midst of the brothers and said (the crowd of persons was all together about one hundred and twenty):
Acts 2:41 (NWT) - 41 Therefore those who embraced his word heartily were baptized, and on that day about three thousand souls were added. 42 And they continued devoting themselves to the teaching of the apostles and to sharing [with one another], to taking of meals and to prayers.
The WTS often points to Acts 1:15 as the beginning of the Christian Congregation since that's when Holy Spirit was poured out on Jesus disciples. If accurate statistics were that important, why didn't someone take an accurate count. A group of 120 isn't that large. Even if no one thought it was important at the time, certainly the accurate number would have come to the Bible writer under insipration if it was vital. Point is, it didn't really matter if there were 118 or 122. The about 120 number is giving the reader the general impression of how many people were there which is really all that is necessary.
So, the reason time is collected is so that local elders can closely monitor peoples activity in the literature distribution work. Everything a JW does is measured by what's on that time card. When discussing who should be appointed as an elder or ms, the number one item of discussion (in my experience) is the brother's time. If married, the wife also has to be turning in close to 10 hours unless there is a major health problem. Although the scriptures in Tim & Titus are in theory used to determine if a man is spiritually qualified, if he's averaging 8.5 hours in FS, it wouldn't matter if he fit every description of those scriptures, he would still not be used. In meetings reviewing a brother's qualifications, I would (as secretary) sit there with the box the time cards were kept in and pull names as they were mentioned. If their hours were less than 10 on average, the discussion would be over very quickly. All this despite there being no specific mention in the qualifications for servants about a person doing evangelizing work as a requirement.
Also, you can't manage what you don't measure. As Gary & WC said, it's business behavior not religious. The WTS is afraid that if they drop the reporting requirement, people wouldn't go door to door. It's really that simple.