So far my basic understanding about Parser is some kind of DPS measurements that are shared throughout the whole party members.

So my opinion to official parser is, no, please don't implement it into the official patch.

I have played too many competitive games and people trash talk each other because the stats show that someone is not dealing enough damage as they had expected. It's too easy to see someone not dealing enough damage through their uses of spells/skills/abilities. Using dps meter to measure your own damage is fine, but let other teammates, especially highly competitive and toxic people, know about it is just not fun at all.