In the US there is one more fundamental issue that needs to be addressed: the use of local school funding in school districts. Had schools been properly funded with more funds going to schools that need more resources (I.e schools where parents don't have higher education get more money per student than schools where they do) then having grades/tests as a qualification for free can be done without discriminating.
Perhaps even more needs to be spent, or the money is spent the wrong way? It would otherwise seem as though DC students are impossible to teach - which seems odd.
But in 90% of cases throwing money at it will help most problems a politician will face. More teachers or better teachers is doable without more money but it's hard. That means you need better school administrators that will attract and develop good teachers - but it's the same argument again - how will you get those?
The objection might be that it's not the most efficient use of money - which depending on your political views might be more or less terrible.
Despite the numerous issues with the american primary/secondary education system, I'd imagine you'd struggle to find many arguing that making secondary education free to everyone (qualified or not) wasn't a net benefit for the US.
It is my personal feeling that the entrance exams that used to exist as a barrier to secondary education were awful and unfair. Everyone should have a right to choose their direction, instead of being told you have to start a job/family. Based on the success of eliminating that barrier, I feel opening up university/college to everyone should be the goal of any civilized society.