Harmy said:

If I want to track the subs movement, it's sort of a package deal, you can't track something less, it just doesn't work that way. I would have to create the shake artificially in order to make the subs less shaky.

Perhaps in those scenes that have burned in subs, the sub shake would look more natural if the shake in the rest of the image were also maintained.

The point is that if both the frame and the subs are wobbling independently, but limited to some small range, stabilizing the entire thing based on ONE of the two wobbles can cause the other wobble to increase. That would happen at each instant where the wobble of one was opposite the wobble of the other. At that moment, if you stabilize one, the wobble of the other is lengthened.

So, if you don't want to decrease the wobble of the one that isn't being stabilized, then the only way to avoid that is to not stabilize the other.