I work outside in Florida, and the heat is sometimes unbearable. But if a breeze hits me, it makes it much more tolerable. There are some days where there is high heat and humidity, and a steady wind. Those days are much less uncomfortable than similar days with no wind. If we are trying to determine the apparent temperature, shouldn't wind speed be included in that calculation?
All weather agencies record ‘ambient temperature’— how warm the air is in the shade and sheltered from the wind. This is done by placing weather recording instruments in a Stevenson Screen. The height above ground that Stevenson Screens are placed is between 1.25 and 2 m (4 ft 1 in and 6 ft 7 in). By using this approach weather readings from around the world can be regarded being consistent and relatable.
When weather forecasters produce a temperature forecast they try to produce a number that will be similar to what would be recorded by instruments in a Stevenson Screen.
Knowing the effect humidity and wind has on how humans feel temperature most weather agencies also try to forecast the apparent temperature. In colder parts of the world, agencies issue the forecast temperature and the wind chill factor. This isn't generally done for warmer regions, partly because predicting wind speeds and wind consistency can be difficult.
Edit 14 September 2021
Apparent temperatures help delineate thermal stress, or how hazardous to human health that thermal condition actually is. Which is why high ambient temperatures are often accompanied with a "wet-bulb temperature" (aka misery index). This better defines how hazardous the high temperature is to humans. On the low end, wind chill temperature does the same thing but for cold temperatures.
Since thermal comfort is entirely subjective, it's not a measurable property that might carry any meaning.
The question is how one would define a heat index, and one could do that in many different ways that would all make sense:
The way the heat index is defined is for people sitting in the shade where they are not exposed to wind. That's a reasonable approach as it is not an uncommon situation for people to be in such situations.
One could define the heat index by taking wind into account. That too, would be a reasonable definition, but people are not all that often in places that have (i) shade, (ii) are exposed to ambient wind at the same time: If you're in a house or forest, you're generally not exposed to the ambient wind -- there might be a breeze, but its strength will very much depend on where exactly you currently are. If you're out where the wind will hit you, you're more likely than not also in the sun.
In other words, defining a "heat index" involves making some subjective choices about what you think matters to the people who are interested in knowing what tomorrow's heat index will actually be.