Good post above.
I use, or used to use, HPF to clean the signal up so other pedals along the chain work better, or at least , to my ears. When i had my micro Thumpinator at the start of my pedal board, I definitely noticed my drive and phaser pedals were more responsive and less muddy. Less inaudible energy that could effect how other pedals behave. Well worth using.
Ive never played loud enough that my speaker cones are dancing around, so the ‘speaker protection’ feature was never one i would benefit from. I dont slap and pop and my Comp is evening things out anyway.
Going back to the Stomp, even though it does have global HPF, like the global EQ, its last in the signal chain, so maybe not as much use as using a HPF (or Parametic) block at the start of the chain.