Sorry but that is just does not make sense at all. First, tons of kids do pageants, you can't just go around knocking out all the competition. Second, there will always be someone who is just as good as you if not better, just because you "get rid" of one person doesn't mean there won't be someone at the next pageant who can beat you.
But the biggest reason the pageant mom theory doesn't make sense, is that jonbenet was not competitive. She just wasn't. She was new, she only had a few titles, and she never supremed anything as far as I recall, she just won her age group a few times. She wasn't well known and she didn't have any major titles.
She was not what we call package kids. Package kids are "very facial" (silly pageant term for being pretty) and they have the clothes, the photos, and the modeling. Now, she was gorgeous, so she had that..but being pretty in a child beauty pageant actually won't help you a bit if you go in dressed all wrong and not knowing the modeling stuff. You have to have the whole package. A girl who isn't as pretty will almost always win over a gorgeous girl if the less pretty girl has better photos, costumes, and modeling.
Patsy dressed jonbenet all wrong and clothes are a huge thing in pageants. Jonbenet needed someone else besides Patsy to design her outfits.
Also, Jonbenet didn't have as good photos as the other girls and - this is a big one - her pro am modeling was awful. Sorry but it was. And in the 4-6 age group, pro am is really what separated out the winners from the losers. Pro am was a huge thing in the pageants back then. You had to be perfect.
Girls don't even do pro am anymore, though. My daughter does pageants now and she's never even learned it.