I think there is merit to all sides of the discussion. For starters, there is true cost in heating a pool by just a couple degrees, most noticeable on the power bill or gas bill if doing so every day, as it does add up. Even without an active heater, a couple degrees per night can contribute to less comfy swimming, even as the nightly loss diminishes as the pool gets cooler each subsequent night. So the issue can matter, to at least some of us. It makes perfect sense that agitated water will be more vulnerable to heat loss, whether by wind or by pump, surely exacerbated by any waterfalls. And yes there are many factors, among them water temperature, air temp, humidity, season, wind, rainfall, many others discussed in many threads. Conversely, it also makes sense that allowing most of the warmer water to migrate to the top will also add more quickly to heat loss / evaporation, all things being equal and regardless of weather. With extensive background information it is argued on
The Palmer Flowreversal X-Body Module Pool Flowreversal Technology Replaces Mark Urban Flowreversal Valves (and discussed in other TFP threads) that you can save up to 1/3 the heating cost simply by pushing the warmer water to the bottom of the pool. So perhaps the question becomes more about how the two competing factors offset one another. For example, if you run a low cost low speed pump at night that pushes colder water to the top, would that result in net less daily heat loss? And would the cost of the pump runtime offset the cost of heating? Separate from the costs, better mixing would surely minimize the complaints from the occasional swimmer who notices the thermocline when jumping into an unmixed pool, if that matters to anyone - LOL. I have fielded that 'complaint' from time to time, even if it's quite the "first-world problem"
In my case I stumbled into a poor man's solution to flow reversal, which I admit is a digression because it does not answer whether to run the pump at night, sorry.... I have a simple setup with just one 2-speed pump that almost always runs on low. Formerly I had most water coming from the skimmer, very little from the main drain, and most output going to the spa to achieve a fairly large spa overflow waterfall. Therefore, little water from the main drain and little water outlet through the pool side ports. The thermocline affect was substantial, especially during the cooler seasons when using the heater. By making the simple valve adjustments to take half the water from the main drain and output more of that (cooler) water through the poolside ports, the thermocline almost completely disappeared! There is a small sacrifice to skimmer efficiency, and the spa waterfall is slowed substantially - but I now enjoy the less noisy waterfall and the pool stays mixed. Perhaps I should run an experiment to see if running the pump at night results in less loss - if only the weather were exactly the same every night. Right now I get about 40 GPM from my $200 2-speed cheap pump (on low), so I guess the skimmer is pulling 20 of that, 20 from the main drain, and 20 out the spa, 20 out the poolside ports. Cost of pump runtime could be further reduced by going with a VS pump on an even lower speed, if it weren't for the cost of the VS pumps - which also seem trouble-riddled (I had one years ago) versus my $200 pump that seems to last for about only four years. I guess discussion of pump cost and reliability belongs elsewhere
Hope all that adds something to the discussion!