Thanks for clarifying that.
The coupling should not show any more slop in either direction. In other words, it's not tapered. If it was, it would ride up and bind on the male splines, and you would lose your plunge. Gotta have that plunge. Look at the female splines carefully. Are they nice and square, or are they "tented"/look like triangles with flat tops? Is there a ridge going around the inside center of the coupler? These an taper are classic signs of a worn coupler.