Long time reader, first time posting.
Part of the problem I see with the idea of sharing designs follows along the “slippery slope” argument. Where does it stop? If we are going to provide kids with ideas why not designs? Why not the (custom) parts? If we give them the parts, why don’t we assemble it for them? Maybe we should just outsource the design/assembly and order a robot?

They can still compete with it. If the students aren't designing things, what are they doing?
In the end, maybe a team doesn’t have the *best* design, or the *best* idea, but next year they will learn more from their experiences when they can look back and discover how and why they made that *decision*. Now, with that said, I don’t think there is a single team within FIRST that wouldn’t bend over backwards to help any rookie team to design/implement their own ideas, but giving them your design would take away that aspect of the learning process from a team that probably needs it most.
Every team has their own philosophy, strategy and attitude. Every design decision involves some cost-vs-benefit consequence and this need to be evaluated by each team. What is “best” for one team may not be right for another team. Help people learn to solve problems; don’t give them the solution.
I also wanted to mention that yes, FIRST is about getting students excited about math, science and engineering (first and foremost). What is MORE exciting than a group of students designing that small competitive advantage (on their own) that takes them to the national championship?
I haven’t been with FRIST for as long as many of the people that I work with, but I have noticed an amazing trend in my 3 years: The more you expect from the students, the more they will accomplish.