I actually don't understand the $3/head part without any examples for the smaller state portion. If a state matches $2-3 then the difference with $7 is negligible.
Beyond this, I want to add that, if we're complaining about the overhead and staff, Chipotle (ignoring recent ecoli outbreaks) and similar have very fresh options ->$6.
From a more corporate standpoint, at $7 a meal, schools are entering competition with "gourmet" fast food options, of which 15-30% is going towards profit margins.
If mall food courts at all compete nutritionally with school lunches, then, at $6-$7 a meal, schools should charge (at market, not cost) for the space and restaurants should have profit margins.
Beyond this, I want to add that, if we're complaining about the overhead and staff, Chipotle (ignoring recent ecoli outbreaks) and similar have very fresh options ->$6.