Please begin by reading this previous Mr. Smarty Plants answer, as well as following any links in that answer to other material. Once you have read all of those anwers, we would summarize our take on this situation.
1. What do you want to keep? Our decision would be the live oaks, they are the most valuable part of your landscaping, as far as we are concerned.
2. No, untended debris will not magically turn into mulch. It will stack up, blow around, and where it piles up will attract insects, rodents, snakes looking for a snack and general trash.
3. A motte of live oaks is risky, in that Oak Wilt can not only enter a tree via damage to the bark (hedge trimmer, weed eater, pruning, etc) but if one tree becomes infected, it will travel to the other trees in the motte via intertwined roots.
Until you have read all the references and considered the options, you won't be able to make an informed decision. Since we are from West Texas where the ground cover is cactus and the trees are scraggly mesquites, we would vote for the trees and stop trying to grow stuff under them. Neither trees nor underplantings are likely to thrive under those conditions.