There are multiple ways you can solve the problem of who gets to go to the most desired school. You can do it via tuition fees and let money decide who goes to the best school. You can do tests to have the best students go to the best school. You can also do random assignments.
Neither of those are “better” from an ethical perspective.
If you let money decide or do tests you lose the statistical benefits of randomization. I don’t understand how you see no ethical problem in ignoring preferences or not matching best students with best schools, perhaps I misunderstand you.
There are multiple ways you can solve the problem of who gets to go to the most desired school. You can do it via tuition fees and let money decide who goes to the best school. You can do tests to have the best students go to the best school. You can also do random assignments.
Neither of those are “better” from an ethical perspective.
If you let money decide or do tests you lose the statistical benefits of randomization. I don’t understand how you see no ethical problem in ignoring preferences or not matching best students with best schools, perhaps I misunderstand you.
Yes of course, you need the randomization.
If you want an equal society that it’s impotant that poor students also get good teachers.