That's an interesting idea, it sound like that could work.
I think simply limiting the number of eliminations would solve the problem as well.
My own experience in going to jury duty several times (and being eliminated each time) is that the lawyers question every one in the jury pool and then use the answers to get rid of anyone who has any knowledge or opinion of anything relating to the case.
One was a civil case, where an older lady was suing a restaurant for damages after she slipped and fell on a wet floor. Her lawyer asked every potential juror if they had any knowledge of the law or lawsuits, or how restaurants operated, or a whole list of other things that would demonstrate an opinion on anything relevant. He then went through and eliminated all but the few who answered every question with "Uh, I don't know about that stuff."
Perhaps, but grouping jurors would make if harder to eliminate some of the people who really should be on a jury. Indeed, an interesting irony is that a pool might have someone each side very much wants and someone they very much don't; both people would be eliminated if they were selected separately, but both parties might be willing to tolerate both people if they thought the juror they liked benefitted them more than the one they disliked benefitted the opposing party.