Are propellers obsolete?
Propellers are not obsolete by any measure.

The jet engine offers two important advantages over propeller aircraft- higher speed and better fuel economy over long range. However, for low speeds and shorter routes, propeller (tuboprop) aircraft are better.

Also, for light GA aircraft, jet aircraft is prohibitively expensive to purchase and maintain. Among other things, the higher speeds associated with jet aircraft make them unsuitable for use in GA. Also, every jet pilot is first trained in propeller aircraft; in fact, airline pilots should have a minimum prior experience before piloting jet aircraft.