See, there's this little thing in the law called conflict of interest. You don't hire a lawyer who is currently representing your adversary in another matter or who has represented your adversary in a similar matter in the past. You don't let your adversary be represented by one of your former lawyers in a similar matter.
And you don't hire a mediator when your adversary is a current client of the mediator!
Sheesh! Sure, let's let Putin broker a deal between us and his client to get rid of the chemical weapons that Russia sold Assad to begin with!
Yeah, that's the ticket!