this should not be classified as another "How do I remove watermarks from my footage" discussion. However I will initially use this exact "problem" to illustrate my point and get to serious compositing situations later on.
We stay with the watermarks for now.
Let's assume that we want to remove a watermark or another semi-transparent object from a video. Content aware fill, blurring or similar approaches won't do the job convincingly. So the next thing we can think of is to recreate the watermark, put it on top of our footage and somehow use arithmetic blending modes like "subtract" or a color-difference key in order to make it disappear. But none of those ways offer the required math unfortunately. I created a test project where I added a watermark (a simple shape with 30% opacity) over a video. I precomped both as "footage", and then used another instance of that watermark on top of that to negate the first nested watermark again. I basically tried to restore the original image with blending modes and the color-difference key but failed. You're still able to identify the pixels that were affected by the process of adding and subtracting the watermark. They just stood out with difference in brightness, contrast or color. Of course you can tweak results with color correction. But well, this is more trial and error than a sophisticated and elegant way of doing it.
It feels like there should be a feature or workflow for this. Something like a negative/backwards compose blending mode, which can - in my example - be used on the top layer (the second copy of the watermark) to blend out its counterpart from the precomposed layer below. So the top watermark layer on which the blending mode is active, just tells the program what unwanted color had been added to the footage below. And it reverses this blending operation to restore the original image.
You could go even further and do this for more blending modes. Maybe you notice that the watermark was put over the video using the blend mode "add". So there can be an option that lets the user chose, which blend mode was used and should be negated.
I don't know if I am oversimplifying this but I guess all parameters for this in order to work are there. We have the watermark affected footage on the one hand. On the other hand the top layer provides information on the watermarks shape, color and opacity. Can't we use this to undo the blending operation with some math?
I guess the quality of the result would depend on how well you could recreate the watermark/object. And of course color quantization would increasingly appear, when the opacity of the watermark was high.
Where could this be useful?
This could be a great alternative to content aware fill when dealing with unwanted semi-transparent foreground objects like lens flares, lens dust, even windows that you shot through etc. In some cases you could just roughly repaint those objects on a seperate layer with this blend mode active and watch them disappear.
Sometimes, you might even be able to use the foreground objects themselves without having to repaint them. This example is the best I could come up with:
Let's assume your lens was dirty when you finally got your eagerly planned 2minutes long take right. So instead of doing it the 56th time you try to fight the dirt in post-production. Of course you can't clone stamp every frame so you use the same camera to make a photo in front of a greenscreen to get the same dirt on a transparent backgound. When something like this blending mode existed, you could now use this layer on top of your footage to get rid of the dust.
Let me know if something like this already exists or my thinking process has logical flaws. There obviously has to be something difficult about this. I am sure they would have implemented it otherwise.