I think telling a kid that they can't compete in a meet across the country is idiotic for several reasons.
They're paying their own way - it costs the school district nothing.
They will have a chance to face better competition than they would in Missouri. This is indisputable. Even if there are 1-2 people that could push them that's much, much different than getting in a race where you have 10-15 people that will push you.
They will have the chance to visit a new place. I think this is big. For a Midwestern kid to have the chance to go to California for a few days has educational value. It absolutely does. I went to Mt. SAC in college. It's the only time I've been to California. It was a good experience. I've done a lot of travelling for track to places I'd never have visited otherwise.
The teammates would *want* them to leave the team behind to go to this meet. At least if they're worth a crap. I remember we had a kid on my team who went to the Mobile Meet of Champions and it was a big deal. He got beat, ran a great time, and it motivated us to try to qualify for the meet ourselves. My senior year we had 4 kids qualify, including myself. Good teammates want to see their teammates compete.