First of all students that do well only allow the academic statistics for that school to be higher giving the school a better reputation so they deserve compensation. Also, too many good students' hard work and efforts go unnoticed and some of the really good students may be poor but not get full rides to college so they deserve to be helped from schools.
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If students get money for doing well they will try harder. With something to gain for doing well everyone will be smart because they want money. Also they wont have to ask their parents for money when they go to the mall or anywhere else. In the future the students will be smarter because of the incentive they got during their school days.
Students will receive scholarships for doing well in school, so they do get money for their hard work. The basic function of schools is to not beg kids into doing well. They provide the tools necessary to achieve a good career- that pays great. It is up to the students to try, and their reward shall be nothing more than a good career.
It's a student's JOB to do well in school. It's absurd that this generation thinks they should be rewarded for accomplishing tasks that they are supposed to do or that are completely banal or menial. Your education serves to prepare you for a future career- that should be all the motivation you need.
Though in a way, they already do pay children for doing well. Scholarships, loans, grants, and financial aid is offered to students who can perform well in classes. I do not think students should be handed money for doing well in school. Hopefully, they'll be able to make more than enough money with the education they received.