Rejected Seats in Government Schools

Last year at this time I was going through a similar feeling and almost the same thought when I wrote "The Best School in Bhutan" where I was trying to differentiate my definition of best school and the definition people and even the authorities have put together. Nothing changed ever since but it brought personal gratification, having figured out the foolishness with which people hunger for reputation and glamour.
Education Ministry defines Class XI intake capacity every year, based on which the qualification mark is set but the recent trend of brilliant students choosing private schools over government school raises one important concern: has the government studied and considered the number of qualified students not take their privileges and therefore leaving seats in government school vacant, which could be otherwise given to students who ran short by a few points? I am of the opinion that we should keep at least over 100 students in standby, who could be considered in government schools after private school admissions are over.
There are students with brilliant marks who are welcomed into private schools and there are students with brilliant parents who can take their kids to private school for so many reasons despite having qualified but on the down side there are students who neither have brilliant marks nor have brilliant parents, for them it's the end of their schooling life. Giving away those seats rejected by the lucky students to those for whom the road has ended would be godly. No less than 100 seats are rejected every year, which could other wise change 100 lives forever.

There should be a system in place to find how many more students can each school take after the admissions are over to make full use of government resources, after all a class of 20 students takes as much resources as that of class with 40 students.
A simple example from my school might shed light on the wider picture: 66 students qualified for class XI, of which the top five students (with 85%- 92.8%) have opted to move to private school on special admissions and one has changed school. A few new students came in from other schools but the whole total could only make up for a section of Science and Commerce stream each. One student who want to take up Arts stream had to be moved to Punakha because we didn't have enough students to begin that stream. We have done the same for the last three years in row after we phased out boarding felicities. My school alone has provision for at least 30 Arts students who can put up on their own as day scholars, and I am sure there could be many schools who same capability.This happened not because of our ministry's miscalculation but by the outflow of qualified students to private schools- which of course is not tracked and considered.
How do we track the outflow? What provisions can be created to make maximum use of government schools and give higher education to as many children as possible?