The bad thing about circular preferences is that they make the number you assign to how good an option is ("utility"-ish thing) not be a function). If you have some quantity of X, normally we'd expect that to determine a unique utility. But that only works because utility is a function! If your decision-maker is based off of some "utility"-ish number that isn't single-valued, you could have different utilities correspond to the very same quantity of X.
Your post basically says "getting money pumped would require us to have higher utility even if we just had a lower-probability version of something nice we already had - and since any thinking being knows that utility is a function, they will avoid this silly case once they notice it."
Well, no. If they have circular preferences, they won't be held back by how utility is actually supposed to be a function. They will make the trades, and really truly have a higher number stored under "utility" than they did before they made the trades. You build a robot that has a high utility if it drives off a cliff, and the robot doesn't go "wait, this sounds like a bad idea. Maybe I should take up needlepoint instead." It drives off the cliff. You build a decision-making system with circular preferences, and it drives of a cliff too.
I thought one usually took the VNM axioms as desiderata and derived that one must have a utility function, rather than the other way round.
Edit: for reasons given in the comments, I don't think the question of what circular preferences actually do is well defined, so this an answer to a wrong question.
If I like Y more than X, at an exchange rate of 0.9Y for 1X, and I like Z more than Y, at an exchange rate of 0.9Z for 1Y, and I like X more than Z, at an exchange rate of 0.9X for 1Z, you might think that given 1X and the ability to trade X for Y at an exchange rate of 0.95Y for 1X, and Y for Z at an exchange rate of 0.95Z for 1Y, and Z for X at an exchange rate of 0.95X for 1Z, I would trade in a circle until I had nothing left.
But actually, if I knew that I had circular preferences, and I knew that if I had 0.95Y I would trade it for (0.95^2)Z, which I would trade for (0.95^3)X, then actually I'd be trading 1X for (0.95^3)X, which I'm obviously not going to do.
Similarly, if the exchange rates are all 1:1, but each trade costs 1 penny, and I care about 1 penny much much less than any of 1X, 1Y, or 1Z, and I trade my X for Y, I know I'm actually going to end up with X - 3 cents, so I won't make the trade.
Unless I can set a Schelling fence, in which case I will end up trading once.
So if instead of being given X, I have a 1/3 chance of each of X, Y, and Z, I would hope I wouldn't set a Schelling fence, because then my 1/3 chance of each thing becomes a 1/3 chance of each thing minus the trading penalty. So maybe I'd want to be bad at precommitments, or would I precommit not to precommit?