There are 4 questions in the original post:
Why does no one use a Buddipole as an Inverted V?
I think it would also bring the impedance closer to 50 ohms which would eliminate the balun requirement, right?
Am I overlooking some key detail here?
Why is this not a more popular configuration?
There are good answers given for question 2, but not for the others. Reason is probably that questions 1/3/4 are quite speculative.
- Why does no one use a Buddipole as an Inverted V?
"no one" probably is an assumption which is speculative. However I must say that I have experience with the Buddipole. I have "bended down" the elements. I cannot recall if the results were any different then the elements horizontal. While never really experimented or measured it, I am not sure about either advandtages or disadvantages of such.
However to say that "no one" uses this, is probably an overstretch
- Am I overlooking some key detail here?
I believe that in order to answer that you need to experiment, measure, and probably apply complex math's to answer such a question. As the Buddipole itself is a compromise antenna, there are many design factors to take into account, which makes the math on detail even more complex.
Chances are that some detail is indeed overlooked, simplisticly speaking. (no disrespect to OP)
- Why is this not a more popular configuration?
This would be speculative, but in my opinion; if you need an inverted V, you need to get the feedpoint up higher than traditionally done with the Buddipole. And while you have the feedpoint higher, you may as well run a half-wave (two quarter wave) wires, to have a normal inverted V.
I have done it, I cannot recall any difference vs the normal dipole config. Saying that, I was not looking or executing any measurements either, so if there was a difference then I probably would not have noticed it. Other than that; I would guess you need to "just try it" and experience yourself.