I’ve always been a bit ambivalent about the three-fold model.
The biggest problem with it is when people consider the three elements as incompatible. Every RPGer uses all of the three approaches...just in varying amounts. Nigh every RPG supports all three approaches...just in varying amounts.
Arguably a healthy RPG must support all three.
Not that I really know what I mean by “healthy”. (^_^) This is thinking out loud after all.