Thanks. I didn't know about this. There are what seemed to me to be clear explanations in Wikipedia. This made for a very welcome respite from reading about the coronavirus over breakfast.
Ted, I think this boils down to an automated method for doing things that people already suggested. I'll try to explain. Correct me if I go astray.
First, we need to avoid the term "global contrast enhancement", since CLAHE is essentially an automated, localized, global contrast enhancement, and "localized global" doesn't on the face of it make a lot of sense. So, let's use a mathematical term for global contrast enhancement: histogram equalization. I'll call it HE to save typing. This refers to making the y values (the heights of the bars) in the histogram more nearly equal, that is, pushing down the peaks to make the distribution more nearly uniform. Pushing down the peaks spreads out the histogram, i.e., increases "global contrast".
The problem with applying HE globally--e.g., by moving the black and white points--is that it will affect different regions differently. Adaptive HE bases the equalization function for any pixel on the distribution of values in a nearby region, not in the distribution across the entire image.
But AHE too has a limitation (apart from the fact that it performs the adaptation based purely on mathematics, not on the intent of the photographer): it can enhance noise if the histogram is too peaked. When the histogram is peaked, there is a very high level of contrast in some regions. CLAHE limits the HE in those regions.
A standard workflow includes adjustments of this sort, although more in tune with the photographer's intent and less mathematically consistent. CLAHE, of course, doesn't include several of the steps noted above (midtone contrast, microcontrast, dodging, burning).
What I found useful about this exercise is that it made me aware of a limitation of my own postprocessing. My local tonality adjustments are primarily dodging, burning, and mid-tone contrast, with an occasional dab of microcontrast. I realized that I rarely try HE locally, e.g., by masking an adjustment of white and black points with a levels tool. Another arrow in the quiver.