That also completely ignores the fact that what you propose would deepen the existing structural inequalities for students, and presupposes that schools are and should remain stratified by income. I vehemently disagree with this unstated premise.
What you are suggesting would be politically very complicated to implement. Also, one need to take into account the characteristics of the district:
https://www.bostonpublicschools.org/cms/lib/MA01906464/Centr...
66% of the students are economically disadvantaged.
Additionally, a lot of schools have both "rich" and "poor" parents, but still need to have a unique time.
Adding money into the mix, when there's a large difference of means between families, adds a level of incentive that shouldn't be there -- one that has nothing to do with the district's goal of providing an equal education to all its students.
When the district looks at the results at the end of the year, and all the poor kids have poor grades/attendance because they were all in the worst time slots, they can't say "well, at least the parents are slightly richer because of this, from the secondary trading market." Rather, based on the objectives they are concerned with, they may have just made inequality even worse.
</snark>
... I also took economics in college. To me it seems obvious that calling a fanciful solution like this "obvious" except for "human pride" is woefully inaccurate.