I tend to side with the brain plasticity argument for starting young. I think work & other adult responsibilities do contribute, but they can't fully account for the difficulty late starters face by any means.
However, I also believe that anything is possible and that talent can still manifest itself later in life. Adults have some advantages that most kids don't, such as discipline, a better developed sense of logic, more money, etc. Not to mention the adult brain is still quite plastic.
I realize there are more attainable goals for players starting late, and I'd be more inclined to encourage those goals, but the players mentioned so far seem to show that it is POSSIBLE to improve quickly at almost any age.
That line gets trotted out a lot, for many sports / skills, but it's BS.
There are plenty of adults that work hours the same or less than the school + homework equivalent. And some people are wealthy enough that they could just devote themselves to a skill for six months, a year or even indefinitely.
Certainly enough time for it to be clear whether they have any practical chance of ever becoming a GM. Which they won't.
There's no end of people that hit 25 and decide they'd much rather be a concert pianist than do whatever crappy job they're doing. But, unless you've had lessons from a pre-teen age, that door is closed. You need to pick an instrument or skill where you won't be competing against people who've practiced all their lives.
Not to mention that they probably wouldn't have had the necessary talent even if they HAD started young. Most people who start playing the piano or chess as kids never make it to that level either. So you have to start young, AND have the talent.