Why is the time measurement in football(soccer) not handled exact like in basketball?
In football, there is a strong tradition that the referee is responsible and accountable for every single decision. This is due to the fact that historically (and even at the lowest levels of the game at present) there was only one neutral official present at a game. Tasking a single official with stopping and starting a clock every time the ball went out as well as supervising and indicating the restart of play would make officiating a very difficult task, hence why it is a discretionary process.
Furthermore, additional time was added in football only to combat deliberate time-wasting, and time lost due to injuries, substitutions and disciplinary action. It was never intended to be used to add on time simply due to the ball being out of play. Up until that point, a match was exactly two periods of 45 minutes, and this included when the ball was out of play. This is still the way it is today. Law 7.3 - The Duration of the Match, Allowance for time lost:
Allowance is made by the referee in each half for all time lost in that half through:
- assessment and/or removal of injured players
- wasting time
- disciplinary sanctions
- stoppages for drinks or other medical reasons permitted by competition rules
- any other cause, including any significant delay to a restart (e.g. goal celebrations)
IFAB, the organisation responsible for changes to the Laws of the Game, up until recently, only met annually and required a 75% supermajority to change any Law. As a result, changes to the Laws have always been very minor. This is why, in spite of there being better timing technology available and more budget to train and pay a separate timekeeper at the highest levels of the game, this area of the game hasn't changed since additional time was introduced decades ago in 1987.
However, as of 2014, this has changed, with IFAB now having two panels that consistently are trialling and studying the impact of changes to the Laws through the year. The recommendations are presented to IFAB, leaving IFAB's members to more or less rubber stamp new changes. It is possible that the method of timing at the highest levels of the game may change in the near future, even though it seems unlikely that it will change at the amateur level.
It is worth noting in some amateur competitions, due to scheduling constraints, there is no allowance for added time at all.