One of my players is running a one-shot for 20th level characters. It looks like I'm going to be playing a 20th level monk.

I am looking at the Way of the Kensei.

Whether it's a Kensei or some other flavor of monk, it looks like as the martial arts die exceeds the die of various weapons, it becomes relatively unimportant what melee monk weapon a monk is wielding, they all do the same damage.

In other words, if a steakknife were to count as a monk weapon, it's of the same effectiveness as a rapier, assuming they're both piercing.

So here's my question, other than damage type, as the monk's level increases, thereby negating the difference in the damage die of different weapons, does it make any difference which melee monk weapon a monk wields?