I think it depends on whether you are hired as a web dev or web designer and what the CLIENT WANTS. Most of the time, when a client wants a website, all he really wants is just that: a website.
That’s why I don’t really understand what you mean by this: "However, this is definitely not what a client will want. "
I mean, why not? If all he wants is a website, why would he care?
Especially if it is a non-tech savvy person, he / she won’t care if it’s built from the ground up, using some kind of framework or whatever. Most people just want it to look good and don’t really care for the inner workings.
The only thing that he might want though, is the ability “to change stuff” by him-/herself which most of the time means including some kind of CMS, like mentioned earlier. In this case you should use something like Wordpress and should NOT try to reinvent the wheel, coming up with you own CMS. It’s nice for personal project, but if you are doing client work, you want to be able to pump out websites as fast as possible.
But yeah, if you were hired as a web dev, then the focus could very well be on the tech side of things.
In any case, each client is different and has different needs. So you really can’t know in advance what a client wants or doesn’t want and should just talk to your (potential) client. Simple as that.