Just yesterday I was doing some research on the state of education in my home state of California, starting with a transcript of a 2003 Morrow Report TV program titled "From first to worst." The rough gist is that California for many years was mandated to allocate approximately equal (and generally inadequate!) funding between districts to correct inequalities of opportunity between school districts. Originally, this was done by adjusting how much the state kicked in above the local district funding; after Prop 13 it became mostly a question of state allocation, since districts could no longer effectively raise their own funds.
Foundations arose as a way for parents to ensure proper funding in districts that were lucky enough to have the donors. So, thank goodness that some districts haven't fallen through the floor, but we're back in the unequal situation we were in before.
Since that 2003 report, charter schools and an update to the funding policy called the "Local Control Funding Formula" have tried to address some of the shortcomings of the equal-across-the-board policy (namely, woefully inadequate funding for districts with greater low-income and english-learning challenges), but our state still funds in the low middle of the pack or at the dirt bottom of state spending per pupil, depending on whether you take cost of living into account.
LBJ's foundation would seem to have arisen along similar lines: like CA, the state is not doing nearly enough to support its public schools, so private citizens have to try to fill the gap through philanthropy. This is great for the children of Akron, but the limitations are clear: it's one school in one corner of the state! I hope this is a shot across the bow that convinces people that raising taxes to fund education properly is not the end-all boondoggle that so many people seem to think it is. A superstar per school doesn't sound scalable to me.