Although, if I'm understanding properly, the increased MA from a different lever or grip position wouldn't help braking if the force is being absorbed by a flexing caliper arm, rather than being transferred into the pads?
I don't think that is right. An action must be balanced by a reaction, so if we visualise a flexible arm/cable/hanger/pad as a simple spring, irrespective of the stiffness of the spring all else being equal the force on the other end of the spring should not be affected by the stiffness of the spring.
What a weak spring in the system will do, is to cause your lever to bottom out at the bars before you can exert the same force on the lever/rim. I think flex in the brake caliper arms is seldom if ever the chief culprit of that being allowed to happen.
You can test my proposition, perhaps, by watching how much farther you can pull the lever after the pads have just made contact with the rim. It will be quite a lot, and I believe mostly due to cable outer compression, usually.
Do brake pads compress to any significant degree? If so do some brands compress less than others?
Such compression would give the same effect - calliper arms moving when everything else is supposedly fixed.
Indeed everything in the brake system flex/compress, to a certain degree. In fact this is what gives a brake system modulation - if you have a brake system where everything is rock hard and incompressible then the brake will act like an on-off switch, not exactly what one wants. The other extreme is allowing lever bottoming out at the bars, also not what one wants either. What one wants is a progressive application of braking force as you pull the levers, with the levers never bottoming out even as you pull as hard as you can - this is achieved by a balance of system compressibility and system MA.
If system MA is too large, a lot of travel at the lever will deliver only a tiny amount of movement at the pads - so while the rim may be gripped by a powerful force the system is not fault tolerant in terms of wheel trueness, pad wear and cabling compressibility, your lever will bottom out easily before the pads can do their work.
If the system MA is too small, your levers are unlikely to bottom out, but you can pull as hard on the levers as you like and the force of the pads on the rim will still be puny, due to inadequate leverage of the force your hand applies to the lever.
I don't know about bending brake callipers, but I had one bike where I could flex the seat stays by applying the brakes hard!
As I mentioned above every action must be balanced by a reaction. If you have a powerful V brake with bosses on long thin seat stays then the stays will have to resist the force on the pads, exerted at ~6x how hard you can pull the levers. The longer the distance between the brake bosses and seat stay end supports, the more flex of the stays at the bosses will be, since the deflection of a simple cantilever is proportional to the cube of the distance to its end supports.
