Is there a reason for the z-axis M5 drive nut to be super loose on the lead screw?
It's probably intentional. Threaded rods are almost never perfectly straight. If the nut is rigidly coupled to the carriage, then the slightest deviation in the screw will either cause it to bind up or appear as artifacts (e.g. z-wobble) in the print. By making the nut slightly loose, it can move around a bit to compensate for wobble. See e.g. this design and this design for how this is commonly implemented in other printers.