Ill start off simple with the great and powerful wiki:
Both an increase in
temperature, decrease in
atmospheric pressure, and, to a much lesser degree, increase in
humidity will cause an increase in density altitude. In hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude.
And then i can prove it with my ballistic calculator (Here is AB Analytics):
59F
28.92
0% RH
DA = 1159
59F
28.92
50% RH
DA = 1271
Try it on any DA Calculator. Here is a link for one:
https://wahiduddin.net/calc/calc_hp_abs.htm
The change is minute. in reality it can be ignored, but to say RH isn't part of the equation is 100% wrong. By setting RH to 50 at all times in your BC you cut the error in half at its most extreme. say RH was zero and you have it set at 50, thats 50% of the error if you had it set to 100%. I encourage you to try it.
I know that aviation formula well. There are also 2 or 3 other quick ways to guesstimate DA. in fact there is another thread here where myself and a few other aviators hash it out. Even ICAO standard atmosphere has a RH component....29.92, 59F and 0% RH. there is a reason for that, that equals 0 feet DA (actually 2 feet but for all intensive purposes its 0). if you increase just the RH to say 75%, your DA is now 165. So it absolutely is part of the official mathematical equation. This page has a long scientific explanation...
https://wahiduddin.net/calc/density_altitude.htm
Again, absolutely nothing wrong with the formula you shared. For what we do its more than accurate enough. Just know, RH matters.