Most of the rig forces will be transmitted along this centre pod. So basically the are no bridles or forestay to flex the hulls.
However, there will be no difference in flexing due to "walking the waves". As such the stiffness difference could be very marginal. Afterall the rig loads to tend to behave as a static pretensioned spring setup. As such they do not alter the stiffness of platform, they just reposition the flexing situation to a different operating point.
Example:
Hang a weight on a spring and measure its stiffness. This can also be done by measuring the oscillation frequency as that is proportional will the stiffness of the whole system.
No reposition this system to the horizontal plane so the force of gravity is taken out of the equation. Measure the stiffness again (frequency) you will find that they are the same.
Basically, adding a static force to a spring setup will not alter the stiffness of the system, it will only change the position of the weight and thus the average position of the weight when it oscillates.
Your other points are of course quite to the point. 3 and 4 mm wires and a dolphinstriker setup tend to be the lightest and cheapest solution most often. That is why dolphinstrikerless setups and unstayed or partically stayed rig have never really gotten into fashion.
The extra material needed in the hulls to take the bridle loads also doubles up as extra material to make the hulls and platform stiffer.
The conventional beach cat design is pretty well developped. Both in weight, stiffness and costs (cheap).
Wouter