an ASSET
It's an asset against squishies (i.e. what she's designed to kill) but not against bruisers/tanks. Poppy really struggles to take them down unless she's fed.
She is unable to be damaged or cc'd for 8 FULL SECONDS by more than one champion
Yep but unless she can push you into a wall she can't do much damage in that time.
Mana is not a poppy weakness- don't spam charge, buy flask, rush sheen
Common misconception, flask's mana regen is basically negligible (3 extra Qs), as is Sheen's. Also if you don't use charge you will get out traded. More importantly, Poppy's base mana and mana regen is extremely low, she will continue to run out of mana after using 3 or so full combos in the late game.
super spammable in terms of mana
She only has enough base mana to use it 5-6 times. 9 times if she has Flask, although realistically speaking she should save mana so she can use charge as an escape.
Sorry, if you're just looking at mana costs without looking at her resources and making these badly theorycrafted assumptions I really can't bother continuing this argument. I've seen Poppy players in high Elo and these arguments I'm making are based off of experience. Poppy is a difficult champion to win with, if she gets fed she's terrifying but against competent players it's hard to get to that point.