You are also missing the point here. You can't get the same for bitcoin cash as you can for a bitcoin. So no they don't use or have the same history after the fork and they aren't the same which is why one is 4 times more worth than the other.

Of course you cant get the same for them! It is expected that a fork that creates new coins out of thin air will lead to cheaper coins.

And so scarcity still exists which was the original point I made and which was being challenged.

Each coin has a unique history. You can create as many forks of bitcoin as you want it doesn't change the fact that there is only one bitcoin.