Allowing your daughter to spend some of her earnings on an activity with her friends IS teaching her to spend wisely, whereas making her work and save all of her money for her chasuna and beyond (for example) will likely lead to tremendous resentment.
All humans need rewards and it is not reasonable to expect a 14 year old to work now (foregoing not only this activity with her friends but the free time she would otherwise have) and see the benefit in many years. By allowing her to spend some money now, she immediately sees the value in working. It’s tremendously empowering to a child (to anyone!) to know that they did something productive, and your daughter will see an immediate pay-off of her hard work.