Scribe, I have a question for you. Assume a session is 4 hours, give or take. Usually, half an hour is burned with late players, unprepared players, players setting up at the table, just general greetings with one another, and the DM doing a recap. Now, of the remaining time, how much of a typical session (and I mean on average, over say, 10 sessions) do you think is reasonable to delve into the psycho-socio differences between the different party members? D&D is built around encounters, be they combat or otherwise, with OUTSIDE triggers. Not conflicts within the party.
I am old school. My games never, ever focused on whether Bob feels motivated to cut off Timmy's hand, because Timmy would never be in the party to start with (Thieves that stole from the party in the olden days and said "It is what my char would do" lasted about 10 minutes). The party was much more focused on the 7 headed Hyrdra in front of them as opposed to whether some sentient swan that mates for life can stand being in the same party as a Half-Orc with no wives but 10 children from 10 different mothers. (Yes, I was in a campaign where that was how the player portrayed their Half-Orc).