[Concept] New forms of damage

So currently with the league of legends, we have 4 types of damage. That is right we have the four following type.

Physical damage: Reduced by Armor, damage resist, and shields.

Magic damage: Reduced by Magic Resist, damage resist, and shields.

True damage: Ignores armor, magic resist, and damage resist. Reduced by shields.

Pure damage: Produced by fountain lazer. Same as true damage but ignores invulnerability and revive effects.

Now while there is a bit of variety in the damage types here, I was thinking of perhaps adding more. Right now league does have a good system for damage so why add more to the formula? Well by adding more forms of damage it can help improve older champions, introduce newer champion diversity, and ever grant new options for items. Though what are these new forms of damage? Well let's get to it.

Introducing, Puncture and Piercing damage. What they do is rather simple.

Puncture damage: Is treated as physical damage. Ignores shields. Reduced by armor and damage resist.

Piercing damage: Is treated as magical damage. Ignores shields. Reduced by magic resist and damage resist.

Each damage respectively represents physical and magical, so there isn't any need to add new resistances. Both of these damages will simply ignore shields placed on the targets. Though I am curious to what others think of the idea in concept. Give me your thoughts.