I can see what you mean, but I don’t think so. In Brazil there are people of every possible skin colour and this has been the case for many years. In the past people thought that in the end, everyone in Brazil would have a similar skin colour somewhere in the middle. It hasn’t happened.
It is something that could happen– though it’s not very likely. Our hair colour is defined by our genes. We know that over time the number of gene variants that appear also changes– which means the levels of ginger, blonde, brown and black hair changes.
We know that the only reasons genes ‘die out’ and become extinct is if they mean a person has a survival disadvantage. There’s nothing yet to suggest that the colour of your hair impacts whether you survive or not, so it’s unlikely the genes will disappear… So we’re probably going to remain having lots of different hair colours in the population!