Back in the 90's I worked on a robot for a pen manufacturer customer. They wanted to simulate nib wear by having a robot write cursive script continuously for hundreds of hours at a time, in a reproducible way.
If I remember correctly, the robot we developed was around 70cm tall, a tripod with the pen suspended on rods from near the apex. The motors were close to the top, one each for the x and y axis, using the long rod to amplify the speed and range of travel of the limited travel motors (voice coil, IIRC) we were using.
As others suggested, in order to be fast enough it had to be be incredibly lightweight. The low payload weight (just a pen) made this just about possible, but to get that speed sacrifices in positional accuracy had to be made with the technology available at the time.
These days we wouldn't have the control issues we did back then (integer PID parameters with the National instruments motor controller we were using, left our system at most marginally stable most of the time, forcing us to cut back the speed to retain stability) but the fundamental limitations of torque, speed, range of travel, precision and cost are always going to be difficult to balance, and unusual requirements in one of these aspects can push the component cost sky high.
There are lots more options available now though, from flexture stages, piezo walk or stack actuators, smaller, more precise lightweight linear motors, but all of these options are going to be expensive, far beyond most hobby budgets.
If you go for a Cartesian robot design, rather than a traditional 'arm', 50 micron accuracy is not too difficult/expensive if your range of movement is not too high. Even relatively cheap fused deposition 3d printers can get 10um step size (not accuracy). Much below 10 micron accuracy gets tough unless your range of movement is very restricted though.