There are a few different things that can impact the material needs. A bare king may have one set of material requirements but if the losing side has some material, the winning side may need less due to blocked squares.
For example, with a bare king, two bishops can't checkmate without their king or other material to restrict squares.
There are also smothered mates where a single piece can deliver mate.
Normally we tend to think of the question "Can I mate with the pieces I have?"
I'd like to turn that question on it's ear.
What combination of two pieces can NOT force checkmate by themselves without the assistance of a King or third piece?
Another way to think of the question, what is the maximum point-count for any combination of two pieces that is unable to deliver mate by themselves?
It's fairly obvious a Queen + Rook, Queen + Bishop, or two Rooks can. Two knights can not.
This question has probably been analyzed and documented somewhere. If you know the source I'd like to read it.
The issue could vary according to the specific position on the board. I recently played a fun game where the initiative swung back and forth several times. What I thought was sufficient fire-power proved insufficient. The common theme was neither side had quite enough fire power or mobility within cramped quarters to put the enemy King down until more help could be brought in to mop up. Perpetual check was possible for both sides but we each played all-out for a win until a time preasure mistake decided the issue.