Everything is absolutely correct. However, if a CC is really hurting one--steep annual fees, monthly fees, et al.--then replacing it with a better CC (which you secure FIRST) often makes a lot of sense.
Closing a CC reduces your overall available CL. Replacing it, even if you're replacing CC#1 with CC#2, and they have the exact same CL, does make a lot of sense when CC#1 is costing you.
One can do a before and after analysis of one's overall and individual CC util. It's possible one could have one's overall and individual CC util in the 1-9 range, then close a CC, and keep one's overal util in the 1-9 range. If one has other CCs, then replacement may not be necessary.