The answer is partly tradition, partly perception, partly "who cares".
In 4 seconds unless you have a really really hometown "scoreboard" operator there has never been any evidence of anyone having the time to stop the clock based on a mishap. It has never happened in major college football or the NFL.
The accepted answer is lacking in basics of football knowledge.
What has to happen in four seconds to "need" the four seconds on the clock:
- There has to be a gaffe or mishap. You would not try to stop the clock if everything was working as normal.
- Mishap #1 would be a bad snap that is low/wide and uncatchable. The ball is snapped, the holder has to get the ball, declare themselves down **, and then call a timeout - and the timeout has to be recognized before the scoreboard hits zero. This has NEVER happened. Note: That only on Field Goal tries can a player gather the ball on their knees and then be active in the play. This allotment is only for the holder. The reason why I mention this is when the holder is gather the bad snap, they are not down. "But they could just call a timeout". Nope can't call a timeout when the play isn't over. At all levels the holder would have to gather the ball and get off the knee and then take a knee or give themselves up. This would take way more than four seconds.
- Mishap #1 - same bad snap low/wide. But this time kicker gathers it. Almost impossible. Maybe - big maybe - if the snapper one hopped the ball on a skip to the kicker and he took a knee and called timeout at the same time, this could be pulled off in less than four seconds. But kickers aren't toe kickers anymore and start over to the side. So even this 1 in 10,000 shot turns into 1 in a million - if the kicker is heady enough to field, down, and call the timeout.
- Mishap #2 - ball is snapped high. Kicker could catch this and down it. Same issue as before but with the height thing the ball is in the air longer and the kicker has further to go to give himself up. Never happened, won't happen in 4 seconds.
- Mishap #3 - ball is not snapped really at all - ball hits centers leg or something. First this might get blown for penalty (and clock is still ticking and game can end on offensive penalty). If it doesn't, again no way an offensive lineman recovers the ball, shows that he has possession and calls a timeout in four seconds. Never happened, never will.
Tradition - Going back to games in the 60s (we have video + FG kickers better) the end of game timeout was generally 3 or 4 seconds. Note that the goal posts were at the goal line then so shorter field goals could cross the plane in 3 seconds with a quick finger in the scoreboard.
Perception - If there is a mishap (bad snap) during the try the coach does not want to get blamed for not having the ability to try again. This is where "alamoot's" answer is lacking football knowledge. Yes the coaches may call it for the perception of his reasoning but if you talk to a coach (like me) there is no way in the world your team will call a time out in that time frame. So in the coaching world it is covering your ass from Tuesday morning QBs.
Who Cares - What if I tell my players to call it at 4 seconds or 1 second? We get ONE FG try - not two or do overs. It doesn't matter when we call it unless we call it so soon that the time doesn't run out and we have to do a kickoff - which is the reason to let the clock down as far as possible. If it is a 30+ yard FG try it takes 3 seconds and usually clock is ran for another second - 1.2-1.5 until kick, and about 1.5 for ball to clear goalposts.
The only other "reason" is..
referees - this does not hold at the NFL or big college level but this is real. Junior football, high school, small college... The referee crews are all over the place. Some are great, some are incompetent, and some are blatantly favoring one team. You simply don't call a timeout with 1-2 seconds left with these crews and allow controversy. Even doing high school games with a good referee crew I will hold up a big "T" with my hands to the entire stadium when calling a timeout if the clock is at the end of any quarter.
Four seconds is probably a pretty safe time in that you get your kick, other team probably doesn't get a kickoff, you can take no fault if bad snap, and you don't have a clock controversy before the kick. It has nothing to do with getting time for another kick.