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Why not just pick the color for the customer and ensure there aren't duplicates within the same block or so?

I guess you could do both? Yet still allowing them to pick a color not yet taken within a certain distance could work.

Why?

Just pick it for them. Don't present the user with choices that have no or negative consequences.

Choice is not always good.

Having the choice would probably be useful for colourblind users since some colours would appear more distinct than others.

You could say the same with lack of choice, but someone answered why it might be an issue if you don't have a choice available.