Team applications: Yes, or no?

I've been in the works of organizing our team for next year, and a subject I've come across is team applications. Mainly applications at the beginning of the year for potential students to fill out, so they can get reviewed and either accepted or denied.

While I think this would be useful of solving the team's problem of finding and keeping people serious about robotics, I also feel that this would go against FIRST, since we're not really inspiring others if we turn them down (Turn downs would only be for explicit reasons, most likely to keep seriousness and productivity on the team, and unproductiveness out).

Should I go with making my team the most efficient it can be, bettering the experience for those on it, or should I try to involve everyone, so they may get the chance to become inspired?

What are your thoughts on team applications, and why?