Your observation about roll inertia is correct: Winglets add proportionally more roll inertia for their small increase in L/D, and this increase exists only for the higher range of lift coefficients. At low lift coefficients (think cruise), when the induced drag is low, they add more friction drag and reduce the L/D overall.
There are three aspects to maneuverability:
- How quickly can you accelerate into a roll? Here the added inertia of winglets reduces roll acceleration
- How high is the maximum sustained turn rate? This is determined by the maximum lift at zero sink rate, and here winglets are helping. Especially when mounted to low aspect ratio wings.
- How high is the maximum turn rate? Now only lift counts, and the increased drag is compensated by an increased sink rate. Again, winglets help a little, but less than with the sustained turn rate.
Now look at the time any fighter will spend around 1g (hint: Something close to 100%) and how much is spent at high lift coefficients, like when turning tightly in air combat. Winglets would help in the turn (and I think Ethan's opinion is wrong), but be a source of drag for the rest of the mission. Adding winglets would require to increase the fuel volume to prevent a reduction in flight time and range.
Normally, winglets are only used on highly loaded, high-aspect ratio wings when their L/D at a rather high lift coefficient needs to be pushed up even more. Highly maneuverable configurations are less concerned with single-percentage increases in L/D for a small part of the flight, and in order to improve turn performance, increasing wing span is much more effective. But that increases roll inertia and roll damping, so fighters use low-aspect ratio wings and compensate their higher drag in a turn with more powerful engines. Note that the trend in fighter aspect ratios went down with the improving thrust-to-weight ratio of jet engines.
Now that is the reason why you don't see winglets on fighter jets: They would lower L/D for most of the flight. To perform the same mission, the fighter without winglets can be made smaller.
But let's make no mistake: Low aspect ratio configurations gain the most from winglets: They were essential on the Hermes re-entry vehicle project to give it enough L/D for a successful flare.