First of all, I recommend clearing away the moral language (value, good, and must) unless you want certain perennial moral controversies to muddy the waters.

Example phrasings of the case you may be trying to make:

Bayesian predictions made from (100% certain) information set {N}U{M} are usually more accurate than those made from {N} alone

I suppose this is true.

Bayesian predictions made from (100% certain) information set {N}U{M} are always more accurate than those made from {N} alone

If you've ever done a jigsaw puzzle, you can probably think of a counterexample to this.