What if the shavepate wanted to cause chaos to rise up, No matter who gets poisoned someone’s gonna be pissed and the fighting is gonna start up again. Maybe he wanted to have the others burn themselves out and then use the brazen beasts to install himself higher than he could ever be under Dany

Assassinating people randomly and hoping it leads to a situation in which you’re in charge is a terrible plan – Littlefinger killed very carefully chosen people and carefully built up favors to get where he is, but even then it was difficult.

Random killing doesn’t necessarily mean the Shavepate’s in control. Indeed, with the Yunkish army at the gates of Meereen, chaos quite likely leads to Meereen falling just like Astapor, and then he’s a head on a spike if he’s lucky.