I second David L11229's opinion. Rope that still contains the core is not only stiff and much harder to work with, but when rope is "cored" (meaning the core has been removed) it moves and flows in a much more visually appealing way than rope that still contains the core. It's hard to explain why, but the cored rope just looks more "magical." Additionally, the cored rope cuts far more easily if you are doing a cut and restored rope routine.
Bonus tip: There actually are scissors on the market that are especially meant for cutting rope and that do the job with one clean cut, as opposed to having to munch away at the rope with regular scissors, which looks awkward, and again, detracts from the magicality. I get both my high quality cored cotton rope in bulk, as well as the special scissors, here:
https://www.baroniantrading.com