Yes,time offers a sense of maturity, but is capable of pushing to a younger age if not held back with preconceived beliefs. If one does not believe great things can be done by an 11 year old, they will not give that person the opportunity to prove it. Only when that person gets old enough to prove themselves on their own do they get a chance. That's unfortunate.
Interesting. Our experience of a unit without preconceived expectations is that scouts earn self recognition awards later in their scouting career rather than earlier because they are busy with the more gratifying activities of maturing with the team (the team being the Patrol, troop, PLC, Crew, Leadership Training, OA, and so forth). In other words, when a boy knows he can earn the Eagle for himself anytime, he spends less time on activities that are less gratifying like the Eagle requirements and more time working to build the team to a maximum efficiency. As a result those scouts tend to get awarded with self recognition honors (like Eagle) toward the end of their troop career, not the beginning.
As has been said, what boys of this age enjoy the most in their life is proving themselves in the challenges of higher maturity. The challenge for the adults are recognizing each boys need for more challenge and providing challenges for him everyday as long as he is in the troop.
But part of growing in maturity is practicing the traits of the scout law in the decisions during their scouting activities. The more decisions a scout makes during activities, the more he will grow from reflecting on the results of those decisions. That is how continued character maturity that is so highly praised of Eagles is developed.
Typically scouts who are not bound by outside expectations, as stosh points out, are more mature Eagles because they have a well rounded maturity that was gained over a longer time from a broader range of scouting activities than the minimum activities required for earning the Eagle. Those are the scouts who are typically leaders in the PLC, OA, crew development and young scout development. Those are the guys the young scouts trust and idolize because they are always seen moving the program forward and treating everyone with respect.
But I caution that even the outside expectation of young scouts performing equal to older scouts can shackle a boys experience in the program. Very very rarely will you meet an 11 year old SPL who has the maturity and skills of a well rounded 16 year old SPL. A troop program trying to prove otherwise is typically a very limited program and is equivalent to an Eagle mill.