I've worked with several square tapers and have never encountered this issue.
I have a MTB with square taper spindle fastened by a bolt (not a nut). The left crankarm fell off during use. Upon inspection, the crank bolt was stripped because only 3-4mm of the threading penetrated into the spindle before it was tight. I thought this was odd and possibly due to a slightly deformed crank arm.
So I bought a new Shimano Alivio crankset. The same thing happens! The right crank arm (along with chainrings) fits onto both the left and right end of the spindle quite well, giving plenty of room for the bolt threads to grasp. But using the left crank arm on either side, it only goes in half way before it is tight, leaving the bolt very little threads to grasp the spindle.
This has been true for 2 cranksets already. So I pulled the left crank arm off another MTB. This one fits perfectly into the spindle! And the 2 cranksets' left crank arm have trouble with this MTB spindle as well.
I feel I must be doing something wrong. How can the left crank arm leave so much space while the right crank arm (of the same crankset) fit perfectly... for 2 different cranksets?
If what I've described is not clear, I can take photos. In short, the spindle only fits halfway into the left crankarm shaft, but all the way into the right.