let them enjoy the sport at whatever level they want. Unless is able to pay for unlimited privates (or owns a gym), though, there will come a point where they will max out of recreational classes and won't be able to progress with skills.
Some people simply go through life learning things for themselves only. They have no desire to show the world their accomplishments and that's OK. But I would also want to be sure something else is not stopping the gymnast from moving to competitive gymnastics before just letting it be.