This post contains spoilers from Game Of Thrones Season 7, Episode 5. While the growing relationship between Jon Snow and Daenerys Targaryen has been the focus of the audience, it hasn't been the King In The North's highest priority. Like the hardheaded bastard he is, Snow came with one focus: to get dragonglass and people to believe in the Night King. And that mission just got a major boost when a raven arrives: Jon knows the Night King is coming.
If we're looking for major milestones in the growing alliance between the Dragon Queen and the King In The North, this scene is it. Nothing says "I trust you" like allowing a man and his second into your war council room, to give a presentation (sans powerpoint thankfully) on why you should consider giving up your lifelong ambition to rule Westeros and turn your entire army and dragons northward to fight something you believed to be a myth 20 minutes ago.
It speaks volumes how far things have come between everyone in two short episodes, that Jon isn't laughed out of the the room, and that everyone, including the newly arrived Jorah, buys into his story of "my brother, who art a tree wizard, hallowed be his visions."
But the fact is, even Dany's forces aren't enough -- and, frankly, she's not totally into this idea. So, when the idea comes up to try and bring Cersei into this "fight against the dead" it seems all a bit convenient to send Jon north to bring back proof.
But it's also not wrong. While no one who's met Cersei is even going to begin to believe she's going to buy into anything that isn't directly playing to her narcissism, Jaime is a different story. Moreover, he actually has the respect (and command) of the Lannister Army.
Everyone might say the goal is talking to Cersei, but the real ticket is getting her brother to agree to join the fight. Tyrion's idea to get Jaime to listen to him is the right one.