Dnil,
Many of the rules of baseball are the way they are because at some point in hisotry, somebody figured a way to get an unfair advantage. An example is the infield fly rule.
As for the "3rd strike not caught" rule, in the 19th century the batter could try to run to first after every last strike -- nobody "struck out", they had to be put out. Back then, the catcher played about 30-40 feet behind the plate and fielded pitches on the bounce. So it wasn't always easy to get the throw to first in time for the out.
But then catchers discovered protective gear. They moved up, right behind the plate and caught piches on the fly. Now it was easy to throw to first in time, or even easier, just reach out an tag the batter.
Then catchers discovered something else. Say there was less than 2 outs and a runner at first. On a third strike, they would throw to SECOND -- getting a force out on the runner at first. Then they would throw to first, getting a "cheap" double play.
So they changed the rules so that when the 3rd strike was caught by the catcher, the batter was automatically out. This prevented the force on the base runners.
Then catchers -- who really are smarter than they look -- started intentionally dropping the 3rd strike. This made the batter a runner and you're back to the possibility of a cheap double play.
So finally, they added another part of the rule -- if first base is occupied with fewer than 2 outs, it doesn't matter it the catcher fields the 3rd strike pitch cleanly or no, the batter is out.