I use the terry scrunchies on Jada and Bogie and they have their hair up every day. I always make sure that the hair at the scalp is loose, just have the band tight around the topknot hair. You sure wouldn't want it tight down to the scalp even for a little while, or at least I wouldn't, I think of a too tight ponytail on my own hair and how sore it makes my scalp after only an hour or so.
I think it is just a personal choice on what works best for you, if you want to cut it off I would. My mom and dad's biewer hates anything in her hair and they keep hers cut off (she is cute as can be that way too)