I haven't watched So You Think You Can Dance for a few years now, but at least when I was watching on a regular basis (seasons 3-6 or so), they did exactly what you're proposing they do, e.g. select highly skilled dancers. There were no "This person is bad at dancing but it's funny to watch them be terrible" getting past more than a round or two at the tryouts, and all of the top 20 contenders each season were legitimately talented and hard working professional-quality dancers. SYTYCD gets their quality (or at least did; again, I haven't watched it for a while) by taking very skilled dancers and pushing them out of their comfort zone; you can be skilled at classical ballet, but can you adjust and pull off a hard-hitting hip hop routine? You can breakdance at BOTY, but can you learn to waltz?

That's a very different type of challenge from "You can't dance, and we want to see if you can learn to dance before you explode", and that's part of why SYTYCD is a good show. Obviously it's a reality show and SYTYCD is going to have some compromises (for example, you might argue that the judge selection is suspect, or that the styles and choreographer choices are limited) but it was honestly pretty close to ideologically pure as you could get; the people who succeeded were the people who were good at dancing, not the people who were good at ballet or contemporary or hip hop or ballroom.