User blog comment:YourPrivateNightmare/The mystery of Blue Ezreal/@comment-6061249-20130613063308/@comment-5686533-20130613103309

gives a unique combinaison of stats that all benefits Blue Ez : health regen (who wouldn't want that ?), mana regen (for spamming spells, 1.4 per second can be powerful), attack damage (35 is still something) and CDR (10% is, again, still something). The 6-40 true damage is just an added benifit, it's not very useful but not totally useless. And all with a cheap price.

For, the mana and mana regen (still 1.4/sec) is helpful to spam spells, and with 2.5k mana, you gain 70 AD; as much as an ; and the toggle will deal (you were correct on that) 150 damage on the first hit.

For, I agree, it is only needed if façing , there is better alternatives.

For its role, Blue Ez is a monster 1v1, but when there is several enemies, he kinda falls off. In fact, he is harder to play than ADC, since, as you have said, he need to split the enemies, but I don't know why he is popular.