There are two choices:
* 13-year olds are old enough to take on the responsibilities of being pro;
* they're not mature enough, yet
In the pro world, we've accepted the former. If we opt for the latter, then that works, too. But it means that we shouldn't have young pros. Or they should be in their own category - "pros that haven't learned the responsibility that comes with the job, yet" or something.
This seems to me to be an ideal summary of the situation.
Now, on that basis, we look at the support for the view that 13-year-olds are mature enough to take on the responsibilities for being pro, we can cite various known behaviours and signs of maturity of this young group:
* They politely say "I was lucky" when they win and "I will try harder in future" when they lose. They may have a tear in private (but so can adults), and they don't rant and rave, have hysterics or tear their opponents' hair out. All of which is behaviour that can be seen in some teenage girls. (But as parents will vouch, this may actually be a sign of maturity of a different kind. The kids are being manipulative, trying to suss out how far they can go with being wilful.)
* They routinely don't spit in their opponents' eyes, don't kick them under the table, don't cough as the opponent decides to play, don't quote obscure rule interpretations, don't burp or fart. In short, they don't misbehave or act obnoxiously in order to get an advantage. Very occasionally there may be a genuine dispute, just as there can be in the adult game (e.g. triple ko occurs: shall we replay or toss a coin?). This is not misbehaviour. This sort of thing is the fault of rules or maladministration.
* They do not go and find a book to look up the next move in a rare joseki the opponent tosses at them. They do not phone a friend for advice. They do not look supplicatingly at a teacher or supporter for a clue as to how to proceed.
In other words, they know all about the whole range of normal, mature behaviour and society's views on cheating. They are mature (or mature enough), their peers have decided.
Yes, of course 13-year-olds will be a different person at 18. An 18-year-old will be a different person at 23 (e.g. he might be married with kids and so learned not to drive like a suicidal maniac). But the 23-year-old, priding himself on his mature outlook in caring for his wife and kids might go out for a night out with the lads, get CV and hug and kill grannie. If grannie survives, she might be a thoroughly mature 80-year-old, but she may also be a bit gaga and so leave her house to her cats instead of her son or daughter. And so on ad infinitum.
Age is not really relevant. What is relevant is your behaviour. That, at least, appears to be the view taken by professional go organisations (whose ethical principles you have to sign up to, by the way.) If you are deemed mature you are deemed to be able to take responsibility for your actions. If you take responsibility, you accept the same penalties as everyone else if you transgress.
You can certainly have a debate about how heavy penalties should be, and take the view that a light penalty is appropriate so that transgressors can have a second chance and learn from their mistakes. Most sports seem to have taken that line. But age of someone deemed "mature enough" shouldn't come into it. Sane penalties, light or heavy, for everyone is the fairest way.