Brushless motors are good at running 10,000RPM or more.
Most brushless motors these days are sensorless so the ESC (Electronic Speed Controller) uses back-EMF to detect what phase needs to be energized when. At slow RPM, there is little to no back-EMF so the ESC has to "guess" and use a "canned routine" until the motor gets up to speed (several hundred RPM).
Turning a stopped brushless motor a few degrees and then stopping again might be possible if you added a quadrature encoder to the shaft, but it would be very difficult to get any accuracy (it will tend to "cog" as the magnets and coils line up) and the motor will tend to freewheel so you'll actively have to power the motor to maintain position.
To make a BLDC motor act like a servo, use an actual servo and remove the brushed DC motor and install a BLDC in it's place. Then you can use the existing gear reduction and potentiometer feedback system. Of course you'll also need to delete the servo controller IC since you will be implementing your own ESC to replace it.