Like for example, I found a steady-op, but I don't like his lighting style personally, so I got someone else for lighting, and the steadiop can stick to that duty. But the steady op was under the impression that he was to be credited for full DP since I knew him first, and he was a DP in other films. Or say how if the sound person doesn't show up, you want to assign someone else in the crew to do the audio?
Does a director have the right to re-assign duties, or is everyone suppose to do the duty they were picked for originally, and that's that? If it is out of line to do that, then that's fine, but I'm not sure.
If it's a union shoot, no. No one can reassign duties, particularly if it's not their job. For instance, if the production is a DGA signee, you cannot get the PM to step in for the First/2nd AD, or for that matter, redesign their role. You cannot get a grip to move an item that is the responsibility of the set decorator... and so on.
Though, I have to assume this isn't a union set since H44 is on set...
It's usually the duty of the department head. If you're replacing a dept head, then it's usually down to the Production Manager, Producer, First AD (usually in that order, at least how I see it) to switch and replace people. I'll also assume you're talking about a feature or a short film and not a TV show. On TV shows, while my knowledge of these is limited, the director wouldn't have the power to make such a call, though the First AD usually would.
More below:
If a Director asked me to DP their film, and I rocked up on set to find someone else DPing it and myself Camera Operating, I'd probably say thanks but no thanks.
You can get an inexperienced person not knowing what they are doing, or an experienced person doing a job lower than the one they currently do, which can be degrading and humiliating to some.
I see this happening repeatedly on local sets and it drives me mad. I see crews bring in a DOP which also brings in his Red camera kit. He gets to set, they reassign him to Camera OP duty and assign the DOP role to someone else. For the life of me, I don't know why he doesn't walk.
Now you're talking a small shoot. On my return to filmmaking, the first set I walked on, the sound guy didn't turn up. The Gaffer stepped up and handled that role, on top of his usual duties. Now, this was a small set with no union rules, so other people stepped in to help where needed.
You can replace people, and if a situation arises where you should replace a person, you should. If you find that you're in a situation where you have to replace a team member, take a good hard look at yourself later and work out how you caused that problem in the first place. If you find yourself blaming others, you still have some growing and learning to do.