The regular assets may be assigned to a different asset class with different features with regard to variance and rate of return. The regular assets also have a different withdrawal structure that makes them subject to a different pattern as you note.

I'd always double check my results against a non-MC analysis where I use 3%, 4% and 5% assumptions about rate of return.

I've specified cautious spending in my Monte Carlo setup. Everything looks fine in the non-MC report. Everything seemingly looks great in the MC report - all graphs go from something fairly horizontal at the Specified Mean Real Return to sloping upward for the 95th percentile. EXCEPT for the MC reports regarding Regular Assets.
Regular Assets are predominately cash. The Specified Mean Real Return for almost all years is completely out of the range (too high) of the MC distribution. Have run the Economics-Based Planning model with the same inputs assuming 3% return and 2.25% inflation and the yearly Regular Assets closely follow the MC Specified Mean Real Returns.
Since the MC runs tells me it is impossible to achieve the Specified Mean Real Return for the Regular Assets, does this invalidate the entire MC analysis? A similar problem was noted by mkinzie on Sun, 08/13/2017 - 17:19, ‘Seeming inconsistency in Monte Carlo reports’.

I don't know. I don't quite understand the value of looking at Regular Assets in the MC analysis or know why we include them. I know that a lot of work has been done on the MC over the past six months and it will show up in the next release in the next three or four weeks. Perhaps it will be addressed there.