Agreed. And I agree on your conclusion with respect to the establishment clause.
But I wasn't addressing the Constitutional issues, only the practical issue of why anyone even cares about swearing to tell the truth in the first place. My point is that you don't even need to consider the Constitutional issues to realize that having any and all witnesses swear on a Bible is simply ridiculous. The issue can and should be decided on that point alone.
That's up to the legislature, I thought we were talking courts. My mistake.