> These are positions where in order for the game to move "forward" both sides would need to individually choose to weaken their position, leaving them playing non-moves until triggering threefold repetition or agreeing to a draw.

Sure, but there's also a whole lot of draws where insufficient material is inevitable. E.g. pawn vs nothing, where the king cannot reach the pawn to defend.

And there's also draws where the only move "forward" doesn't weaken the position, but lead towards an end of insufficient material. E.g. most situations pawn vs. bishop.