Well, I have been involved in some of these situations with photofinishers being shut down due to effluent, and also doing lab tests on the effluents and how to constrain them.
Yes, the volume of sewage is important, but the absolute concentration of ingredients is also important. As an extreme at one end, the sludge becomes so thick it is virtually impossible to treat. On the other end, the volume is so great that the holding tanks can overflow. Both are bad.
But, you miss the point that a huge "plug" of concentrated chemistry can do more damage as it enters the treatment area than a larger more dilute flow. The word here "CAN" is important, because actual tests around the median, not extremes is ambiguous. And, I hasten to add that most of us dump very little due to the size of our operations.
Now, for a specific example of something extreme but possible. A photographer wishes to dispose of his effluent and he lives in a desert area. If he decides to dump it in the desert, should he dump concentrated waste over a small area, or dilute waste over a large area? This hypothetical question has real import on the situation we are considering here. The interesting part is that the concentrated effluent has insufficient volume to be dumped over a large area, but the dilute effluent can be dumped over a large area. The same holds true in a wash. Successive dumps occur with plug flow in the pipes and enter the sewage treatment as blocks of contaminant, but the more dilute continuous wash takes place over longer times.
In practice, as I said, the results are ambiguous due to the low flow from our types of labs.
On another tack, when water is severely limited, then a whole new set of practices hold. In a true desert environment, water is precious for both incoming purposes and outgoing purposes. There are few studies on the exact nature of what should be done in these cases. There are ways to adapt to this using mixed bed resins in which the total water consumed and total effluent remains zero once the system is set up and charged with water. You put in your initial charge of water for all of the processing system and then just drain off the deionized water at the other end and re-use it. The problem is the cost of the resins and the cost of disposal. This was all worked out by myself and others at EK in the 70s BTW.