I currently use 2 different containers depending on cook needs - a 10 qt Fagor duo pressure cooker bottom, or when more space is needed, a Coleman 28-Quart Cooler With Bail Handle. My last few cooks I’ve used the Coleman 28 qt exclusively. I’ve removed the hinges so the cover comes off, and used a 2.5" borer to cut inside one of the 4 inner-lid circles (perfect fit) to drop the Anova Precision in. I then put the lid upside-down on the cooler. This works perfectly, and the cooler is amazing at keeping the temperature. I’m wondering what determines the water volume limitation? Circulation limitations? The water seems to agitate ok from what I’ve seen, and once the unit is cooking at proper temp, even when off, you’re hard pressed, with the lid on, to see a point degree loss - usually a few tenths at best. After a 4 hour cook I turned the unit off (at 140) but kept it sitting there and in an hour it only lost 2/10 of a degree.
By the way, the above pics are of this most recent cook - a scheduled 24 hour cook at 135F for 2 3lb+ beef chuck roasts. Should be done when I get home from work tonight 
I would bet the volume specification is tied to the units ability to heat water in a time the designers specified. Too much volume and the water will take a long time to heat. I also may be related to the units ability to maintain all the water at a consistent temperature. As you exceed the specified limits there will probably be a drop off in performance up to a point where the temperatures vary in the vessel.
I’d tend to agree with your assessment with the caveat though that, with the fully insulated cooler method, it would appear that maintenance is easily achieved (at least with this particular build). Perhaps if someone tried to use like a thin, cheapo, huge tamale stock pot, it might not be able to hold temp - particularly higher temps. I haven’t exceeded 140 in this yet - hopefully this same setup will be able to sustain higher temps without stressing the device - I’ll need to break out the kill-a-watt.
I’ve cooked in a few vessels, but two in particular are relevant here - the super-insulated esky with a tight-fitting hole drilled in the lid very similar to yours, and a thin glass-walled open-top fish tank of similar volume. When cooking vegetables at over 85c, the esky gets to high temperature very quickly and stays there without any problem, but the fish tank took over an hour to get to 80c and couldn’t manage more (eventually I gave up). I’m guessing that Anova took a guess at the average user’s container and ambient temperature to decide on their specifications.