You raise some good questions.
From an advertisers perspective, you use local advertising because your target market has local qualifiers, explicit or implicit- within a local boundary or outside the boundary (like travel or gift buying).
From a searchers standpoint, you look for things locally because your needs, wants, or capabilities may have geographic attributes.
>>"Local Search" sounds like it is design to most benefit local searchers
Sure that is the majority of it. But we live in a mobile age and our consumption be it either restuarants, events, or hotels, et al is mobile. Local search will be in our cars, phones, and pockets. It will be able to better guide our mobile behavior.
There is significantly higher search volume for major cities ~ volume that is disproportionate to population. That is because more choices are available and a disproportionate amount of consumption takes place in these metro areas. This affects ad spend and search.
Also, if you had something to sell that is easily sold nationally ~ and you knew people were predisposed to look for the product on a local level, wouldn't it be wise to reach out to those large local markets in LA, NY, Chicago, etc. or at minimum the major cities in your state or region?
What truly is 'local' is surely a hotly contested area of local search. You can see it being played out on every major local search tool. Like Superpages which gives the top three spots on a geo-vertical results page to nt'l ppc accounts, and who also reserves the entire right side ads to nt'l only. Observe the ugly looking broad match results being pulled into Google and Yahoo Local. On and on. Watch as the national dollars begin to pollute pure local listings that might be more relevant... but less lucrative.