What advantages is gained by building a circuit - opamp based preferably - to debalance a balanced signal, versus just shorting one pin to ground at the input jack?
It depends on what sort of signal is being debalanced. -If you're debalancing the output of a GSSL for example, you must NOT short cold to ground. If you're debalancing an LA2a, you MUST short cold to ground.
Noise rejection. See http://en.wikipedia.org/wiki/Balanced_audio for a short description, or the articles on the Jensen Transformers site, or this article, or several of the threads on this forum which have discussed it in the past.
Probably more appropriate to call it "single-ending" rather than debalancing.
What Keith is probably referring to is that some outputs are simple low impedance differentials which will not be happy if one leg is shorted to ground. Some others may be floating transformer windings or active balanced with cross connected feedback to mimic transformers, that might not pass signal at all or exhibit response/level errors if not terminated properly.
It's not as complicated as it sounds. Most gear designed for wide use is pretty tolerant about how it's terminated.