I know i wouldn't of fit on the right side in my LX3310. I can in the L5460.I have never felt the need to enter my LX4020 cab from the right side, which would be tight having to squeeze past the loader control.
I often access those 3 control levers through the right side door. I have also moved the tractor by pressing gently on the pedal (just enough without hitting the safety switch)when lining up the 3-point.A good reason for having a door on the right side is so you have easy access to the loader control, three point hitch lever, and PTO switch from outside the cab. The safety reason is so you can get out if you accidentally roll the tractor on its left side.