People want to maximize utility, we'll use money as a proxy, people want to maximize money. I suppose there are economic schools of thought that use other proxies for utility, but you seem to be agreeing with me insofar as the primary stand-in for utility is money, and it is a poor one.
No, that was my exact point. In general, economics treats money and utility as distinct. I should've been clearer: money only proxies for utility in behavioral experiments.
Labor supply theory, for example, assumes people maximize utility by choosing a combination of work and leisure. It doesn't assume people work as much as possible (or, maximize their money).