You would have variable speed/direction propellers.
While good in theory I suspect the average servo would wear out in short order under such service. Also the speed would not be very useful for standard propeller sizes that are designed to utilize thousands of rpms. Plastic gears and brushed DC motor do not make for reliable continuous service applications. Possibly by obtaining servos using brushless motors and metal gears such a application is possible, but at much higher cost servos, and still the prop rpm range problem would remain unless one also designed custom really long props.
Lefty