HVLS fans in the summer?

The wind chill effect is very powerful for comfort. Properly located, the fans probably have little effect on stratification close to the ceiling where exhaust fans can still remove hot air. You don't need ten feet of stratified hot air under the roof for any reason.

You need to look at the application and actual conditions.

When temps and humidity are above a certain level, OSHA recommends to NOT blow air on people since it actually makes things worse. I don't recall the the exact temps, may be over 90 or 100F where fans make things worse.

If outdoor air is colder (and drier), it may be better to just bring in outside air.

Those are just examples.

If the wet bulb temperature is above 90F you will not get any evaporative cooling (through sweating), nor cooling through convection or radiation, since the dry bulb temperature will even higher. Core body temperature can't be allowed to rise much above 99F, and skin temperature needs to be 10-15F cooler to get cooling for someone working.

Right. Because if your body is a 98°F and the skin at 90°F (due to sweating) you have a 90°F micro-climate around your skin. If you blow 95°F or warmer air over your body, you heat up that microclimate.

As for stratification (again, very dependent on situation), you should not de-stratify and exhaust air at the top. Like a hole house exhaust fan. but it really only helps if the incoming air is colder.

It all depends.