There are so many variables it is difficult to draw any reliable conclusions about the fate of 13 year old players. Whether they are playing rec or travel, reduced size or full sized diamonds is not significant. They are just too young yet to draw any meaningful conclusions.
The big factor is innate qualities, not learned skills. No matter where you play, your innate quality will not be significantly impacted. NOW HEAR THIS. The higher level of ball you play, the faster your learned skills will develop. But only to the level that your innate ability allows.
There is no learned skill that a rec player with innate qualities cannot pick up on the full sized diamond in the year before HS tryouts. If a player on the full sized diamond shows potential it is then he should be playing with and against the best players that he can. Before that time it is all rec ball.
People dealing in absolutes talking about 13 year olds are in unchartered waters.