Pitch stability is much harder in comparison and I wouldn't even know
where to start. One would need to be a control systems expert.

Pitch stability isn't very difficult if you have pitch sensing and
pitch control. I guess I'm a little bit of a control systems expert
(I've taken control theory courses at the graduate level and designed
and built some oddball control systems) and I could do a pitch control
with no problem. So can the A/P manufacturers. The problem I
described doesn't occur with any 2-axis A/P that I know of, in any
airplane.

The problem is that roll and pitch are dynamically coupled (prove it to
yourself - apply roll input and the nose drops) and the coupling is
different between airplanes, and for a given airplane is likely a
function of mass, cg, inertial moment (controlled mostly by how far
outboard the fuel is), airspeed, angle of bank, etc. Without knowing
any of those things, it's pretty much a given that if there is a
divergent pitch mode (and many planes have one) the A/P will find it
one way or another. What bothers me is not that a given
airplane/autopilot combination can be forced into such a mode, but how
trivially easy it is. No effort has been made to suppress this
undesirable behavior.

If I were going to fix this problem, I would start by having the unit
read the bank at startup, and go into a recovery mode designed for the
airplane, probably involving stabilizing the angle of bank and then
slowly reducing it. Not saying that's a guaranteed fix, but it's
simple and IMO would probably work. BTW, this is simple enough to do
in an analog design, and pretty trivial in software. But there's no
incentive to do it - causing a divergent pitch oscillation by
overcontrol of the roll axis doesn't make an autopilot unairworthy - no
rules cover this.

It may make it unsafe if used in the manner often advocated, but unsafe
does not mean unairworthy (and vice versa).

Michael