Yes, of course, but that's what I mean by problem. Saying people are (bonded rational) utility function maximizers doesn't give us a predictive theory, it just means in a fancy way people do what they do for "reasons", and everyone usually have different set of reasons.
Of course, it's fine as a very-very general fundamental theory, if you then want to study how people's revealed and non-revealed (old names for implicit and explicit) preferences aggregate into a utility function. (There's a whole bunch of math about pairwise comparison matrices. Lately there's some movement in that space about using perturbation to model inconsistencies in preferences, etc.)
Of course, it's fine as a very-very general fundamental theory, if you then want to study how people's revealed and non-revealed (old names for implicit and explicit) preferences aggregate into a utility function. (There's a whole bunch of math about pairwise comparison matrices. Lately there's some movement in that space about using perturbation to model inconsistencies in preferences, etc.)