I’m still failing to see the contradiction: is there anything I have said anywhere that contradicts your conclusion?
Therefore, any action which, over time, costs more than its utility cannot, by your own terms, be rational, Q.E.D.
I define rationality as ‘enhancing long-term net benefit’ (or well-being, or welfare, or any such notion). This can be restated as ‘[an action] not costing, over time, more than its utility’.
But let me try to clarify some of the points above.
I am confused by your use of the terms rationality and utility. For me, utility is merely a measure of the overall benefit experienced as a consequence of a transaction. It is possible to envisage an infinitely large utility, both positive and negative, so there are, in effect, no bounds to this.
I am not sure how dividing utility by cost produces a meaningful value. I would subtract these two quantities. If the difference is positive, the behaviour involving the transaction was rational; if it is negative, it was not. (I don’t think arguing about what exactly zero means makes much sense, since it is not really possible to establish either cost or utility with any accuracy.)
Do you see rationality as a continuous variable, rather than a boolean? For me it is the latter — a behaviour or a choice is either rational (if it enhances overall long-term wellbeing, i.e. the overall utility > the overall cost), or it is not (if it decreases overall long-term wellbeing, i.e. overall utility < overall cost).