Bourdieu didn’t need to propose anything. He proved data in hand that the system was unfair. A quick look at the current situation of France should tell you all you need to know about how effective the system actually is.
But finding ideas is not that hard. We could just get our heads out of our asses and copy what’s done in a country having better results. Spoiler alert, the answer is not a system generalising the structure of military schools to whole areas of higher educations put in place by a military dictatorship to curb the emergence of dissenting elites in the university system. It still baffle me that this has to be pointed to the average French. This country really deserves what it has become.