If a student fights then they are wasting school time in which they could be in a classroom learning or studying. Time for them to go to school is time that is paid for by taxpayer dollars. This means that by fighting, they are using up our money given to the school system for the students to learn. The fine would make up that cost.
I think students having to pay a fine when they get into a fight could be a good idea. I believe that any measure we could take to cut down on fighting and bullying would be worth trying. If a student or a student's parents had to take some fiscal responsibility for their behavior it might curtail fighting a bit.
Yes. Students should pay a fine for fighting in additional to other punishments. If students and or their parents pay a fine, this would deter them from fighting and force them to seek other hopefully productive solutions to disagreements and conflicts. If young people are not taught about consequences to negative behavior, they will run into problems dealing with conflicts later on when they become adults.