Especially, if you plan to go out in the winter. In extremely cold temperatures CLP can freeze.
Additionally, graphite "sticks" to the mast better. Instead of running down your mast and puddling at the base.
CLP is great at high temperatures (when you are firing off a lot of rounds) and at breaking carbon free. Neither of those situations should be encountered by your mast stick to something that is a superior lubricant at regular and low temperature.
I also do not think it would be very easy to raise a mast that was covered in CLP. I imagine it being an exercise in frustration. I think using a dry lubricant like graphite would make raising a mast much easier.
My preference has always been 'nothing'. Graphite is excellent for points mentioned, but I find it overused and very messy.
If a mast is properly cleaned and dried before storing, it makes all the difference. I have pulled open a mast at the Unit before exercise and find someone had it stored wet, and then there is a good chance it will freeze as one piece before deploying it outside in winter.
If the mast is really soaked, then graphite makes little difference in the freezing temps.