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In this answer Ethan makes the following statement concerning winglets on fighter jets:
[Winglets] reduce maneuverability which is why you don't see a winglet on a fighter jet
I could image that adding more weight at the end of the wings increases inertia, reducing maneuverability, but I'm not sure if this is the only reason.
Perhaps there is some aerodynamic phenomenon at play as well?
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:
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.
The effects of winglets on the maneuverability of aircraft is not straightforward, with different effects on various maneuverability parameters.
In the simplest sense, the winglets have the effect of increasing the aspect ratio of the wing. This results in lower roll angular acceleration as a higher moment of inertia needs to be overcome before the movement begins.
The roll rate (at maximum aileron deflection) is slightly greater with winglets, as they increase the local span loading near the wing tips, thereby augmenting aileron effectiveness. This means that smaller aileron deflections are required for a given rolling moment; meaning less drag for a given roll rate and a higher maximum roll rate.
As the winglets increase the L/D ratio, the climb performance is improved.
There are other reasons for the absence of winglets in combat aircraft, such as:
Winglets are optimized for a particular configuration of wing, flight speed and profile and are usually ineffective, and may even have adverse effects on aircraft performance in other situations. For example, the winglet increases profile drag while reducing induced drag; in conditions where profile drag is a major contributor to the total drag, this is a disadvantage.
The winglets will have disastrous effect in supersonic flight due to the added drag.
The thin winglets are prone to flutter problems.
Winglets will add considerably to the radar signature from the most critical angles.
An unsung property of winglets is that they improve yaw stability, which can actually reduce drag, especially for designs which require yaw damping.
Going back to the days of the Sopwith Camel, fighters benefit from instability to turn more effectively. While today's fighters have computers to make them safer, the Camel was very challenging to fly.
Contrary to some opinion, winglets are not a "drag disaster" and were very sucessfully used on the XB-70 design (folded down) to increase the lift coefficient of the delta wing, allowing it to fly at a drag saving lower angle of attack.
