You're absolutely right, earth isn't sphere & earth radius is variable from equator to polar, if you want to get an accurate result you need to get your latitude radius & also distance to your desire SAT first before using this equation. I just put 3964 & 22300 values in order to write the equation & is not exact radius & distance to satellite for other site's.
I know calculation is a hard way to get all these information when you can get them in seconds on the net. but i'm a pilot & flight navigator and I have learned & accustomed to do every job on it's standard way instead of relying on the internet & website's. That's why i rather to solve such given problems through computations. Imagine you need to set up your satellite in the middle of desert with no internet connection, it's not better to do it yourself instead of getting help from other sources?
If you were launching satellites details like the exact radius of the Earth would be of interest, but we are talking about polarity (or even azimuth or elevation) that going to vary by numbers that are much smaller than the resolution of the instruments that are used to aim the dish. The worst-case scenario is that the radius number is off by 11km or 0.15%. The impact on the angle formula is a much smaller percentage yet.
If you think about it, this kind of variance could easily be undone by the sun passing from one side of the dish to the other and the thermal expansion of the materials changing where the dish is pointing.