The entire point of covert asicboost is that it is covert,
I don't think that is true. It's one of the problems with calling it "covert AsicBoost". It gives the false impression that it is "wrong" or "bad" or "secretive".
The entire point of AsicBoost is to generate SHA256 hashes as efficiently as possible. The point of "covert" instead of "overt" is that with "covert" you don't need to make a mess of the block version number (which is better used for actually keeping track of the block version). The fact that it is not easy to tell that a block was mined using the "covert" method is a side effect, and not the point.
Well covert asicboost requires more computing power than overt asicboost. You need to find several merkle roots which collide in the last 32 bits and this requires more computing power and more memory than overt asicboost. That additional requirement makes covert asicboost less efficient than overt asicboost. I would think that a miner would want to use the more efficient overt asicboost method to get the most performance gains as possible rather than using the less efficient and more taxing covert asicboost unless they are trying to hide the fact that they are using asicboost.