You should be very very careful when doing any reasoning on color based on mathematical intuition.
First thing is. Your monitor is not linear! RGB color is not linear. And grayscale is not linear (dot gain can just be different than RGB, but be careful their black and white dont need to match) They are configured to be nonlinear to enable us to use 8 bit per channel color. Even the scientific color mode Lab isn't linear the way you think, its perceptually linear, which isn't the same thing. The whole expectation that the numeric values have some mathematically meaningful interpretation is just wrong.
Programs like Photoshop have 20 years worth of development for them to be what you see is what you get. This means that the very messy process of how human eyes and brains work is factored into this. Including nonlinearness of those systems.
Why would this be beneficial? Well, artists are traditionally humans. And they react to sensory stimulus. So when you have an artist the important bit is that they sense it correctly, numbers be damned.
But this does not fit your use case. That is fine Photoshop isn't even designed for your use case. Possibly you should be using something else like zbrush or mudbox. Anyway the real answer is that if your interested then you can do this all you need is to make a color profile and dot gain that is truly linear.
But beware monsters lie here! Now you are in trouble since you are fighting the purpose of your software. You need to know how to deal with every step from this point forward, in pgotoshop and your entire publishing pipeline there is a chance that any one of those things encodes your linear values in nonlinear. Which you are unlikely to want. Also it becomes problematic to show the picture for you since the interpretation is different from what you think. There is really no good solution here. Explaining everything here would be a good state of the art review for a PhD.