Jose schrieb:

When would an operating control tower not induce class D (or better)
airspace? When would a class D airspace not have a control tower?

I can't give you an example in the USA, but where I live, there are
controlled airports without a control zone.

Controlled airfield means the tower controls the runway. Control zone
means the controller controls the traffic around the airfield. These two
are not nessecarily related. (Although they typically come together.)

Stefan