Nothing about utility maximization model says utility function is unbounded
Yep.
the only mathematical assumptions for a well behaved utility function are U’(x) >= 0, U″(x) ⇐ 0
Utility functions aren’t necessarily over domains that allow their derivatives to be scalar, or even meaningful (my notional u.f., over 4D world-histories or something similar, sure isn’t). Even if one is, or if you’re holding fixed all but one (real-valued) of the parameters, this is far too strong a constraint for non-pathological behavior. E.g., most people’s (notional) utility is presumably strictly decreasing in the number of times they’re hit with a baseball bat, and non-monotonic in the amount of salt on their food.
Yep.
Utility functions aren’t necessarily over domains that allow their derivatives to be scalar, or even meaningful (my notional u.f., over 4D world-histories or something similar, sure isn’t). Even if one is, or if you’re holding fixed all but one (real-valued) of the parameters, this is far too strong a constraint for non-pathological behavior. E.g., most people’s (notional) utility is presumably strictly decreasing in the number of times they’re hit with a baseball bat, and non-monotonic in the amount of salt on their food.