Why use jet engines instead of propellers when designing new airplanes?
Look into Propulsive efficiency (and maybe also this one).  Turboprops have a speed of peak efficiency, which is around mach 0.6 or so.  If you try to go faster, it gets significantly less efficient.  A high bypass turbofan, on the other hand, is most efficient at a higher speed, maybe mach 0.8 - 0.85.  So the simple answer is: we switched from props to jets because people wanted to fly faster but didn't want to burn a lot of extra fuel to do that.