The suction tool is used to dry the area out and make it easier to see and work. A robot could be taught to see through water, but it still needs a dry environment for some work.
And the opposite for others. For example, getting cavities filled in the front of the mouth probably benefits from laying face up so that any saliva that's generated flows back down the throat instead of to the front of the mouth.
I'm guessing a lot of existing techniques and tools have an implicit bias for the patient being face up.
