As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.
But presumably you don't get utility from switching as such, you get utility from having A, B, or C, so if you complete a cycle for free (without me charging you), you have exactly the same utility as when you started, and if I charge you, then when you're back to A, you have lower utility.
If I have utility in the state of the world, as opposed to the transitions between A, B, and C, I don't see how it's possible for me to have cyclic preferences, unless you're claiming that my utility doesn't have ordinality for some reason. If that's the sort of inconsistency in preferences you're referring to, then yes, it's bad, but I don't see how ordinal utility necessitates wireheading.