As a high schooler I can answer this and I can say my work doesn't even compare to that of a professional with a degree, It's very tedious work, most professional web developers find third-party templates to be, well troubling. They have to listen to what their client wants and have to create it for them.
For me, I make websites for myself! I sometimes use templates, professional web devs are masters in front end, as well as back end development, most high schoolers--including myself--pay for a web host. A professional is much much more disciplined, the final product is clean and most of time bug free.
To answer your question, Yes high schoolers can build websites, but there's a lot of things that building a website involves, not just designs, and that is what young web developers lack, and what we strive to learn.
