I've thought it would be nice to see jurors randomly pre-pooled, and lawyers allowed only to eliminate prospective polls.
For example, start with six pools of six jurors and one alternate; both sides are allowed to eliminate two pools for any reason. The remaining two pools try the case.
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."