The usual reason for caisson (I call them drilled piers) caps is to allow the vertical reinforcing in the pier, which is usually in a circular pattern, to develop into the cap AND allow other vertical bars in the cap to extend out the top to develop into the columns or grade beams above, which may be smaller in width than the diameter of the pier.
So its simply a transfer mechanism.
We have sometimes specified additional vertical bars to be set in the top of the raw pier and extend out in a square or rectangular pattern so the grade beam can simply be poured directly over the pier without the additional formed concrete cap. It just takes a good contractor to set these bars properly so you don't have them sticking out the sides of the grade beam.