But if the school has the power to push out the deadwood (and public schools usually don't have that power) then the students who remain in the school don't fall into the hopeless category you describe. For those students, $13,500 should go a long way.
You're assuming that the entire $13,500 actually gets spent in D.C. classrooms. SoftballMominVA has shown on several threads that a good chunk of that money actually goes for lawsuits and to send special education students to extremely expensive private schools because the special education department in D.C. has been incompetent and/or corrupt for years.
An interesting point...the really "top-notch" private schools in the D.C. area, including Sidwell Friends, St. Albans, etc., cost well over $20K per year per student.