The Crimson Binome
Hero
If the rogue doesn't want to go through a locked door, and refuses to pick the lock, then the fighter deciding to pick the lock and go through the door anyway will necessitate splitting the party. Splitting the party is a bad idea - even ignoring the question of overcoming challenges - because the DM can only handle one group at a time. Ergo, to avoid one or more players needing to sit out for extended periods, it is best for everyone to make a character who plays well with others.I don't think your last sentence is true. Certainly not in my experience. To explain the basic idea: if PC 1 is arguing with PC 2, then the players of both PC 1 and PC 2 are involved in the action.
The first one is definitely a thing. The rogue may very well be dead, or otherwise temporarily indisposed, and that's a good reason to have some sort of backup around.That leaves at least two of the possibilities I mentioned available (the fighter being there while the rogue is not; there being two lock that need to be picked simultaneously) and others that I haven't thought of yet.
The second one is difficult to imagine, unless the DM is specifically contriving a situation for it to happen. In all my years, I've never seen a trap or lock which needed to be disabled in two places at once.