This would mean that you client gets in big trouble if the clientname gets changed or the domain gets changed e.g. if its a test setup that goes live as most cms systems store the paths where they are installed in their config files. For that reason we use ID's for the directorys and only the domain name for reasier shell navigation as symlinks.
That would also remove the /folder from website to make subdomain what I think is a stupid way to do it.
Just create a new website instead of a subdomain and you get a new folder for every subdomain which is not inside the web.