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I think for many nurseries, the key person does a bunch of admin work to demonstrate that they're paying attention to your child's development and nurturing it.
From my perspective as a parent in researching this (I'm not a an psych expert), the importance of the key worker system is the child developing strong bonds and attachments to 1-2 individual nursery workers. This is really important in a nursery, where staff turnover is high and I want to feel like my child has one or two anchors to turn to when upset. And also that I have a 1-2 points of contact who I can go to when I have concerns about the child and feel like someone is actually overseeing my DC's emotional needs as well as the other stuff (like EYFS, which is helpful, but less important to me).
Not all parents care about the key worker system and sometimes the nursery will minimize the key worker role and say something like "your child can turn to anybody". It can be important to have a point of view on this if it means something to you, and share that POV with the nursery if you have concerns like the ones you mentioned. The things that you mentioned are completely reasonable to raise.
Also, you can see a lot at the drop-offs and pick-ups in terms of who you're child is naturally bonding with and which staff are taking a genuine interest. Those should be two important things that determine the key worker assignment.