Some characters can be trusted, others can't; and whether they're PC or NPC matters not. I've played characters who will try to turn any situation to their own advantage regardless what it means for anyone else; and I've also played characters who have been on the receiving end of such. It all depends on the specifics of character and situation.
Ona broader scale, one thing I do not generally assume is that real-world ethics and morals fully translate into the game world. Here in the real world we try to be respectful, inclusive, considerate, and all that; while in the D&D game world it's pretty much wild-west law of the jungle when you're in the field and something like "the king's word is the law" when in town.
I am trying to play a game with my friends and we all want to have fun. So we
work together to make sure we all have fun, and we can't have fun if we can't trust each other or if we go all Lord of the Flies on each other. When you're in the field, you need societal rules even more, because you have no one else to rely on other than the other PCs. The only reason your games don't fall apart is for completely meta reasons, because you know it's a group game and not a solo game--in reality, you're not going to go fight the lich-queen with someone you can't trust not to steal from you or stab you in the back.
The camera in the shower wouldn't fly here either.
And yet slavery and charming other PCs is perfectly OK!?
But charming other characters? Won't say it happens all the time but it sure ain't unheard of. PCs routinely charm NPCs in order to a) extract information and-or b) take them into the party as meat shields, and if its good for the goose it's good for the gander: if the situation allows, I'll sometimes have NPCs try to charm PCs. And PCs charming other PCs, often as a non-painful means of keeping them from doing something stupid, is almost a tradition in some parties.
And as I said, that is a
bad thing to do because it takes agency away from those other players.
Rime, my chaotic neutral rogue, often does stupid things. Put a button in her path and she'll push it. The DM loves her because they can guarantee I'll find the plot that way. The other players try to reason with her as to why not to do certain things, and it often works. But the idea of charming her into obediance is anathema to the rest of the party because mind-control is pretty evil. And no, we don't charm NPCs either for exactly that same reason.
Both of these are tangential at best to the question of the party protecting Jocasta more so than they'd protect anyone else, because she's the last of her kind.
And you are
continuing to assume that's the primary or only option with the last mage! If she's a PC, then it's up to the players to decide if they want that party dynamic.
"Well, let's see how much help she is, first; but if she's any use then we'd better do whatever it takes to keep her upright as we ain't gonna get another one if she dies."
And
here you are reducing a PC to a mere tool, rather than as a person. Rime isn't in the party because of her skills as a thief, since she has none besides stealth (Int was her dump stat and many rogue skills in 5e are Int-based; she's a swashbuckler, who rely on Dex and Cha); she's part of the party because she is friend and ally to the other characters. We have nobody who can search for traps with any reliability. We have NPCs with the party because we have befriended them or because they're part of our backstories, not because we hired them for a role.
We've had games where a PC has
not been able to become friend and ally to the characters for whatever reason--typically goals or personality too different--and each time, the player had
chosen to have PC leave and then made a character who
could work with the group. But this is very rare, since we all find a reason to work together.
Your suggestion was that the bodyguard character agree to be hired as such by the last-mage character; and "hired" implies many things: a boss-employee dynamic and authority structure; an expectation by the employee that there will be recompense (i.e., pay) for time spent at this job, perhaps in lieu of a share of treasury; an expectation by the employer that the employee's first loyalty will be to the employer and that the employee will put the boss' interests first, and so on. In other words, a hench.
By "players" here you mean "characters", I assume.
No, I mean players. As in, two players had a discussion about their character ideas and came to the conclusion that it would be a cool party dynamic if one player was the boss and the other was their secretary.
Are these secretaries truly employees of those who they secretary for? I ask because if yes, the boss-employee authority dynamic means there's a situation where one character can legitimately tell another character what to do and expect it to be done. Not every player is going to be cool with giving away that much control over their character; if yours are, that's both cool and IME very unusual.
Yes, they're truly employees. But no, because while the boss can order the secretary around, the secretary's player can
choose whether or not they are going to obey,
and the secretary's player can have a discussion with the boss's player if the boss is getting out of hand with their demands. Because we understand that things like one PC being abusive to another is as much a player issue as it is a character issue, because it involves a player making the choice to act that way. There's no such thing as "it's what my character would do." Your characters are not separate entities over whom you have no control. If they're jerks, it's because you made them that way.
Plus (in my MotW game), the boss is really dependent on the secretary to do things such as pick up the dry cleaning and correct their abysmal spelling and work the phones and make sure there's enough raw meat in the fridge to satisfy the boss after he wolfs out. The power balance is actually equal. It's not just one player ordering another one around.
But switch from that sort of game. Let's pretend we're talking about game where you're in a chain of command. A military game, or something like Star Trek. The players are still
choosing to play in that dynamic. Because it's a group game where the goal is for everyone to have fun, having the captain or commander PC abuse their relationship with the other PCs because they're in charge means that there's a good chance that the other PCs aren't having fun.
Though I have to ask: if you care about them that much then why are you exposing them to the (undeniable!) risks of field adventuring in the first place?
Because they're PCs, and I'm not going to force other players not play their characters. This is what you need to understand, and you seem to refuse to do that.