See, I don't think the President should "come around" to Burnham, she basically said, "You're awesome but not ready, there are a few problems". It would be nice if they both learned new things being each other's foil. And Michael works on her flaws, like any good officer would.
But considering the way Trek (and, tbf, most other shows) have depicted politicians, combined with DSC's tendency to Alway Prove Burnham Right, I'm skeptical.
As an episode, this worked well for me, so I'm undecided between 7 and 8 points.