I don't think this is the case... the reason the fees rose in the first place was because we maxed out the capacity of the Bitcoin network and miners started mining the transactions with the highest fees paid first. Now Segwit is activated as long as the Bitcoin network capacity isn't max out fees will drop, soon as we hit capacity they will start t go up again. This is the same for Bitcoin Cash, soon as we hit the capacity of the network on that miners will start being selective again and fees will go up!