I will just quote this portion. Think your analogy is great in particular when it comes to discussing the differences in rods. You state:
The thing you aren't stating here is that you are now ignoring the force on the end of the cantilever and only looking at tip deflection. I don't see how we can ignore the forcing function on the end of the rod. In a fishing rod scenario, the fish applies this force and that is the answer to the length question and what is more sensitive. The material and rod design is of course important and the second portion of the topic. For the rest of the forum I will go into more detail to explain what I mean.
To visualize this better, a fixed cantilever and end points for variable discussion is shown here:
The tip deflection is defined as:
δ = (FB*L^3)/(3*E*I)
Being we are making the assumption that E, I are the same to make this simpler we can substitute a constant, C.
δB = (FB*L3(AB))/C which you nicely showed we can re-arrange to find which we can re-arrange and solve for the Force at B or FB
FB = δ*C/ L3(AB)
You also shared the smoking gun in the length argument. The moment at point A is defined
MA = FB*L(AB)
By default this states that no matter the force applied at point B that the moment will be stronger the longer the rod is. Your conclusion stated differently when we substitute FB from above, the question of course is why? This is more easily seen for those not wanting to do math without the extra E & I. Sole reason I retyped most of this.
MA = δB*C/ L2(AB)
Here you can see that the moment at A is indeed inversely proportional to the length squared, but the equation MA = FB*L(AB) shows that it is directly proportional. The question is how can you have two completely different conclusions from the same set of equations? The answer is in the stated equation though. The MA that was solved only includes the deflection at point B as it's forcing function and not the force. In other words, if the rods are identical (in E & I) the longer rod will put more force on the fisherman; however, the force felt by the fisherman based on tip deflection is more on a shorter rod and significantly. Of course, when we go back to the original tip deflection equation:
δB = (FB*L3(AB))/C
We can see that the deflection is directly proportional to the cubed length of the rod. Being the moment felt is to the 2nd power based on deflection, but the deflection occuring is to the third power this reinforces the longer rod is more sensitive theory as well....but imagine that, it was conveniently described earlier with a simple equation MA = FB*L(AB)
Of course the final portion of the sensitivity discussion in relation to length is also hidden in fissure's response.
δ = (FB*L^3)/(3*E*I)
We have already nailed down tip deflection, δ, Force & Length,FB*L, but the other key parameters in a sensitivity discussion are E the modulus of elasticity and I the moment of inertia. These cover the shape and materials in the rod. Obviously they have a major effect on tip deflection which we saw above has a cubed relation to length.