I prove this as a mathematical theorem here:

Theorem. Every act of observation has, before you make it, a non-negative expected utility.

Note that the theorem ignores everything that you might expect it to ignore from the formulation: non-rational or non-utility-maximising agents, the cost of acquiring and using the information, the effects of other people knowing you know it, the effects on yourself of knowing you know it (as distinct from merely knowing it and so updating your utility-maximising decisions), etc. etc.

Should I write this up for arXiv? The theorem is not deep, but neither is Aumann's agreement theorem, and that's in a journal.