As long as their diet is reasonable healthy, I see no reason why not to allow it. Not to let it be the only drink, but there are MUCH bigger battles to fight. Back when my dad taught in inner city schools, before adhd medications were so common, he always kept a pot of coffee on in his office. He would pour a cup or two down any of the kids they knew had adhd but the parents couldn't afford the docs or medications. Some kids he gave coffee to before school and at lunch and it seemed to help them.
I would try to limit the Starbucks drink type things as the amount of sugar in them is just unbelievable. Our middle school sold a coffee frozen drink for a while. One of my daughter's friends was sent to the office 7-8 times and to the counselors at least that many times because they thought she was on speed. Before school she would drink 3 large cups of this frozen drink and at lunch she would drink 5-6. Her parents had more money than sense, in my opinion, and gave her an enormous allowance. The school limited the drink to 2 per person per day, but she got other kids to buy them for her. She literally ran around like she was on speed and couldn't sit still, stop talking, etc..... Took a while, but finally the other kids ratted her out and shocked all of the adults. Then someone looked into the calories and sugar per serving and it was 3 times the sugar of any other drink, even of the Starbucks frappuccinno drinks. It also had a huge amount of caffeine, and the lunch room ladies decided it was too unhealthy to serve at school, so they stopped selling it. It was a special fundraiser item for some project of the principal, and he was pretty angry that the lunch ladies wouldn't sell it, but they sold some other item instead.
Other than cases like this, I have no problem with teens and coffee. Few people restrict or think to restrict soda/diet soda, even Mt Dew and Diet Coke which have the highest caffeine of any soft drinks.