This is obviously a fairly touchy subject, but I feel the need to rant on it a little
Yes, in an ideal world every student interested will be part of a team. But this is less than an ideal world. My team has around 20 students in it each year, and we can't safely manage that many students with any less than 5 mentors. There's simply too many things in a shop (with saws, drills, and other things that could cause serious damage) that can go wrong, and one person can't have their eyes everywhere at once. We accept everyone we can get, but our first and largest priority is safety. I'm not sure what we'd do if our team size suddenly doubled. Probably celebrate in public, and cry ourselves to sleep at night trying to figure out how to handle it all.
Yes, there is a lot of stuff people can do on the team. However, how many people can you really support with work throughout the season? Even if you go for all the awards and do all of the "side" work like animation and website, you get to a point where you simply have too many people on a task for it to go smoothly. You can only fit so many people in a shop or around a robot. Each team needs to be able to determine what the appropriate size is for their team - a size they can successfully manage and run. If that means they have to turn some people away each year, then that's tough. Really tough. How do you make that decision?
Well, you start with an application process. You put questions on it and list your expectations for the team. You do your best to design the application to ensure you have as many kids involved as you can manage, and that you're picking the kids who will best support the team throughout the season.
Lets play some hypothetical number games here. Lets say you've determined that you can only support 50 kids on your team, but you have 100 that apply every year. Well, if you require that they're not involved in any other activities during the build season, you can weed out basketball players, theater members, etc. Say that's 30 kids. Now, you require their attendance in off-season events, workshops, and summer camps. You've just lost another 10 kids. You require certain grade levels. There's another 5. By requiring these things, you're helping to narrow down the selection pool to a manageable level, without having the possibility of "playing favorites". This gives you something very clear and obvious to point to when parents complain, and you can have good, scripted descriptions of why each item is necessary. For example, "I'm sorry Mrs. Jones, but we had to deny Timmy's application because he plays basketball. As I'm sure you understand, Basketball takes up a lot of time, but so does robotics. We meet for about 20 hours a week, and many of those meetings conflict with the Basketball practice schedule. With so many students applying to the robotics team each year, we want to make sure that we can provide an environment for those who can be truly dedicated and get the most out of this opportunity."
So, what about fee's? Our team has a fee. A lot of teams have fees. There are fee's to play on sports teams, be a member of the marching band, debate club, or other organizations. They're called activity fees and are fairly common for a lot of different things at schools, especially those that cost money to operate. If you ask for a $200 activity fee each year, just tell the students and parents what they get for it - several hundred hours of interaction, teaching, and experience with professional engineers. You won't even get that paying tens of thousands of dollars each year at college. Most schools also have funds or other ways for financially challenged students to join teams.
In short, how teams manage who joins and who doesn't is really up to the team. There are way to many considerations to be able to look in from outside and say they're doing it wrong. We have some guidelines for students in terms of being allowed to travel with the team or letter, and it's really tough every time you have to give a student "bad news". Just making the decisions is tough. That's why we build our guidelines to be as black and white as possible, which appears to be what you saw.