Stepper Motor Axial Travel under compression

I recently purchase some stepper motors to build a 4 axis foam cutter
CNC. My intent was to directly drive the lead screws via a coupler
interface between the stepper motor and the lead screw. On examination
of the NEM23 type stepper motors, I notice that if you press on the
motor shaft with some moderate pressure, there is some significant
axial travel under compression. Motors were originally outfitted with
a pully drive pinion.

Couple of questions: 1) Is this axial play a normal stepper motor
design feature? 2) How have other folks isolated the lead screw so as
to avoid this axial play under load?

DC