In the same way we almost always display something like "Release Name by Artist Credit" instead of just "Release Name", I think we should display the area name after the place name and consider the area it's in an integral part of the "identity" of the place.

Right now there are 87 places with an area set which have a disambiguation comment. 34 of those are identical to the area name and several more are variants of the area name. That suggests to me that a significant number of cases (assuming the existing behaviour is what we're going to continue to see as more places are added, which seems likely, given that the more we have, the more chance there is of a place sharing its name with another) where people feel places need disambiguating would be resolved simply by displaying the area name more.