Why Shen has such low base HP?

i looked it up and it isnt really low its just mid tier with things like gnar and junglers

A surprising number of champions have seemingly mismatched base stats for their role.

From a mathematical point of view however, let's say you have 50 base HP and your "squishy" counterpart has 100 base hp. If both of you buy an item with 100 HP, your health tripled whereas the squishy only doubled his health. You are more inclined to build defense than your squishy counterpart in this scenario. Let's say you spend your first back on defense and them on offense. Well, because of how most stats in the game work, League is highly multiplicative in many situations. If you start with defense, you tend to want to continue building more defense (say armor), and the same applies to the enemy offense. Mathematically, you have a numbers system that naturally invites champions to build for their role.

this allows them to give him a high hp scaling passive. They fully expect you to stack hp on him.

I think they nerfed his armor scalling a bit too hard tho. He has one of the worst base armor, scalling armor, hp scaling and base scaling in the entire game. I hope they give him some armor scaling sometime.