Especially for the player frame, as many people tend to want to use a dedicated addon for that or are just fine with the vanilla casting bar.

Thats why that is already an option

No it is not:

Player frame options:

General options:

Nowhere is there an option to disable the LunaUnitFrames Castbar, that appears under the player frame or target frame.

I found an option to disable it deep hidden behind a dropdown menu. This is not straight forward at all. Maybe improve the visibility of this option then.

No, but the FAQ and Addons description needs an overhaul. Maybe even a little video introduction to the features.