Kensei monks actually have a reason to use more unarmed strikes than usual- they can opt to use an unarmed strike instead of a weapon attack for one of their Attack action attacks, and they get +2 AC for doing so.
You still have to be *holding* a weapon (the flavor is you're opting to punch/kick/etc. to keep your weapon free for a parry), but on their turn they do have an incentive to do one more unarmed strike/one fewer weapon attack than other monks.