When discussing teens and their sucky writing, let me also note in fairness that there are positively scads of adult writers whose writing sucks as well, some because they only began writing in earnest when they became adults, some because they tried to cruise by on cleverness when they were teens and are paying for it now, and some because, well. Some people are just no damn good at writing and will never be.
I don’t think there’s any one particular time when one passes the suck frontier into non-suckitude; you just get better as you go along and then one day you’re sufficiently good, which is not necessarily the same as being actually good, or good at all aspects of writing. I was sufficiently good at writing at age 22 to get a job doing it; I shudder to think what a novel out of my 22-year-old self would have been like. Likewise, at 38, I’m a better writer than my 28-year-old self, who was a substantially better writer than my 18-year-old self; I hope to Sweet Merry Jesus that my 48-year-old self is an even better writer still.
The ideal situation has a writer continually distancing him or herself from suck. This, however, is not a guaranteed thing, and you have to work at it. It’s called “suck” for a reason. It’ll be happy to pull you back in.