Gouli,
I suggest that the hot-day density dependence reflects nothing more than the relatively marginal nature of helicopter flight. In exchange for those special capabilities, there is a compromise in the ability to carry great loads cheaply.
The power demands to haul vertically upwards are very significant, and when air density is down by about 10% at 30C, as compared with a freezing day, it gets tough. More rotor speed and angle of attack, and more power, wastefully beating up more intense tip vortices, and imparting rotation to the wake is required.
Then again, with fixed wings, the speed at which lift is adequate for flight also depends on the density, although the leeway between getting adequate lift and compressibility of the flow becoming an issue is likely greater.
While different outcomes might be achieved on different days, straying into territory where the outcome is that marginal is probably not a good idea. I would not encourage stalls to be considered as "chaotic". The airflow over the wing is chaotic post-stall, but when the flow breaks down for a certain set of temperature-pressure-humidity-turbulence conditions is very reproduceable. What about the Elmendorf C17 crash, where to paraphrase "the stall warning always sounds here"? It doesn't sound like a message you want to be giving.
Was that a "rolling take off" for a helicopter on wheels, or choosing/being required to accelerate in ground effect? I guess they're effectively the same thing.