I think what you are suggesting is similar to the "dead-beat controller" in discrete-time control literature. While a controller designed with this method can get the position error measured at the sampling times to zero very quickly, it gives no guarantees that the error stays zero between the samples. This means the block could be wildly oscillating around the arrow in reality, but oscillating in such a way that it's exactly under the arrow at the times your digital controller measures it.

This would probably not be a concern in this digital simulator, but such an error can pop up when trying the same thing out in real life.

See slide 17 here for a plot: https://www.slideserve.com/sibyl/finite-settling-time-design

There appears to be a hidden limit on acceleration forces.