Why is poppy allowed to invalidate champions with dashes while not being extremely weak to the rest?

Yes, I just lost lane badly to a Poppy. Yes I'm whining about it.

My problem isn't so much that Poppy beats champions with dashes, it's that she doesn't hard-lose to champions who don't have them. I mean, we're seeing her picked blind in pro-play, that's beyond enough evidence that she's a relatively safe pick against just about anything.

And why? If Poppy was built to deny dashes, you'd think a first pick Poppy should never exist. She should only be strong (or dare I say it, viable) when she's picked in to a team that has dashes (or at least a lane opponent). Yet she functions perfectly well in those scenarios too.

I mean, ignoring her dash-denial, what else does she have that makes her so strong? A dash herself which doubles as a stun if she pushes you into terrain. A movement speed boost A good aoe damage / waveclear ability A hard CC ultimate that can also single-handedly change the course of a teamfight or steal/secure Baron A passive which gives her a basically free lane as she can CS from range and then get a shield to deny damage when she CS's as melee.

To me, that passive sticks out like a sore thumb. It's overloaded. She has so much in her kit to punish enemies without it, yet it sits there to protect her against anyone that would punish her. Why does she get to have her only weakness almost completely covered up while so strongly denying strengths / creating weaknesses in other champions?

As I said, I have no issue with her being a strong counter to mobility. I have no problem with her being a staple COUNTERPICK in the pro scene. I have a huge problem that she's able to do so well against immobile champions too though. She should have some weakness shouldn't she? She shouldn't be a safe blind-pick, she should only really succeed as a counterpick and otherwise be open to some risks if you want to pick her blind? Right?