Well, technically you can hack your way around.
The key is to offset the animation so you can crossfade between this one in and out so the perfect effect for this is Delay RGB with all 3 sliders full on. Then just crossfade the effect at the beginning and end (but dont fade out to 0% otherwise it will bypass the effect). So set the lower values to 0.01%. The effect's opacity playhead/envelope should be set to clip and you are good to go.
In my example I just trimmed my animation to make it 'unloopable' but you can see that this way you can pretty much loop
anything which is not loopable with this effect. The only problem is that the delay RGB might not be 'late' enough but oh well, it works