Earlier quoted context omitted.
Most "analog computers" have been simple, and even if they usually provided the solution of a system of ordinary differential equations, that does not require a control part, making them no more closer to a complete computer than a music box that performs a fixed sequence. I agree that this kind of "analog computers" does not deserve the name of "computer", because they are equivalent only with the "registers + ALU"…
You're describing a "hybrid computer". These were introduced in the late 1950s, combining a digital processor with analog computing units. I don't understand why you and kragen want to redefine standard terms; this seems like a pointless linguistic exercise.
Sometimes it has been applied to the kind of computers mentioned by me, with a digital control part and a completely analog arithmetic part.
However it has also been frequently used to describe what were hybrid arithmetic parts, e.g. which included both digital registers and digital adders and an analog section, for instance with analog integrators, which was used to implement signal processing filters or solving differential equations.
IMO, "hybrid computer" is appropriate only in the second sense, for hybrid arithmetic parts.
The control part of a CPU can be based only on a finite state automaton, so there is no need for any term to communicate this.
On the other hand, the arithmetic part can be digital, analog or hybrid, so it is useful to speak about digital computers, analog computers and hybrid computers, based on that.