I agree that it does not help the image of justice, and yes, I think it hurts it. Whether it's to the extent of disrepute.... I'm not sure I'd go that far, but it certainly is harmful to it.
I think yours is a very interesting suggestion, and it's one that I think should be considered and explored. I have to tell you, I'm a traditionalist. As is apparent to you, I'm old, and it's hard for someone my age to change views and look at new ways of doing things, but I think your suggestion is an excellent one that should be considered.
You're absolutely right: we spend too much time on basic, fundamental matters that at the end of the day are not in dispute. We try to overcome this with very aggressive case management prior to trial. An experienced, persuasive judge can often accomplish it in pre-hearings, but I think it's an area that's well worth examining for legislative change.