For me, a centre line is a handling line, not a mooring line. It means, for example, when queuing for locks, I can walk the boat up easily, plus when single handed doing locks, particularly uphill, I can walk the boat in without having to use a ladder. I sometimes use it for added security (three points of contact) overnight but not tied tightly, just enough to keep the boat near the bank if the front or rear is untied.
My earlier comment (post #22) was when walking the boat up in a queue. The idiot exited the lock at normal cruising speed, and I needed to take a turn around a bollard to save swimming after my boat.