In some places, it is impossible to duplicate a master key, but individual keys to a door can easily be duplicated.
Your metaphor starts falling apart here. Individual keys or child keys that are derived from a master key are unique themselves and can not be "duplicated".Well, I think it's just the context from which we both see this that is different.
Over here in my country, I don't know about other places or other parts of the world but In my area here, from what I've seen and learnt, a child key, that is; keys to each of the doors in a house can be duplicated, there are craftmen who specialize in this job, this helps to have more extras just incase one gets lost or misplaced.
But the master key of the house, that is; the key that unlocks every single door in the house can not be duplicated, I guess this is a security measure put in place to encourage their holders to protect it at all cost, since there is just one of it and there will never be another.
I used this metaphor to explain not because it really tallies, but it gives a simply and easy to understand idea and good representation of the difference between a seed phrase and private key, and why it's impossible to derive a seed phrase from a private key, but possible the other way round.
