Hello @vaishhg,
Thank you for reaching out to us and your comprehensive yet sparse problem description, this really makes things easier for us.
The problem is a bit that you somewhat forgot a crucial part: The scene data :). You provided this:
Create a Cinema 4D scene with a Main take (frame range 0-6)
Create child takes (V, E, R, A) and override the render data's frame range on each (e.g., V: 0-9, E: 0-23, R: 0-13, A: 0-17)
But I cannot recreate a scene with these instructions, unless you meant the second step in a rather metaphorical way (switching the render data itself via takes). I also talked with some of our support specialists, and the consensus seems to be that what you claim to be the case - a scene with take overwritten FROM/TO values - is not possible. What you can do, is create multiple render settings and then activate them via takes.
But Takes are a tricky subject, and I would not rule out that you somehow found a way to create take overrides for parameters of a render data instance. If so, please share the scene. Find also a scene attached which demonstrates what I discussed above: A scene that switches the active render data based on takes. It will print this with your script:
Take 'Main': FRAMEFROM=0, FRAMETO=90
Take '0_45': FRAMEFROM=0, FRAMETO=45
Take '0_90': FRAMEFROM=0, FRAMETO=90
take_renderdata.c4d
So, to formally answer your main question: When my assumptions above are true, your scene is printing the same values because each take does have the same values, as these two parameters are not directly overridable.
Cheers,
Ferdinand