Starfleet also probably thought being on routine scan/explore/catalogue duty wouldn't require Shaw and Seven to be around each other all day every day (like Picard/Riker, Janeway/Chakotay). Maybe Shaw takes day shift, Seven takes night shift. And, as the mission goes on, Starfleet assumes Shaw will slowly work his way through his PTSD seeing Seven and adjusting to her and seeing she's a valuable asset to the crew.let’s not forget, yes he’s a ships Captain. But from the descriptions of the Titan it doesn’t appear to be a front line “major” ship like the Enterprise or a little butt kicker like the Defiant. It’s closer to an explorer ship like Voyager or the Equinox.
so putting a Captain with PTSD with an XO that used to be a Borg (and that command was forced to give a commission too by two influential Admirals) is lower risk, high reward.