While it sounds like a cool project, using servos instead of steppers is just a bunch of added complication, cost and downsides.
But first, let's be realistic: we are extruding plastic at several 0.1mm width. For example a 0.35mm nozzle has to lay down plastic at a minimum of about 0.4mm width to achieve good layer adhesion. So having 4096 steps per rotation on a servo vs 3200 steps on a stepper (200 steps * 16 microsteps) will make zero difference. (Although higher microstepping is also possible at the cost of power output and processing speed.)
Then you add a whole bunch of electronic components, increasing cost and failure points. Brushes in servos wear out, needing replacement. And I'm sorry, but some cheapo small servos from RC cars will not be a replacement for the beefy steppers used in even the cheapest 3d printers. BTW, servos are a major point of fail in RC car, and a decent servo costs several times that of a nice stepper.
Let's also think about what happens if there's a mechanical failure that would trigger a step being lost, for example a stuck bearing. A stepper would simply stop working. A servo would not stop until the encoder wheel reaches its position, so without some added safety system the servo would just commit suicide, burning itself down or chewing up its gears.
Having said all this, my current reprap printer has yet to skip a step after several hundreds of hours of print time. So looking for a solution to a problem that doesn't exist?