The real reason of substandard education is the lack of better lawmakers IMO. And it's an especially hard problem to solve in India.
Its a vicious cycle where uneducated citizens select equally uneducated lawmakers (because susceptible to propaganda/lies easily). The uneducated lawmakers don't have much incentive to improve education, because that will affect their election results, next time around.
And turning to private institutions is of no use. They have neither the good will nor the cash flow to actually do something about this problem...