Apparently Case Western Reserve University Law School thinks it has found a way to make co-deans work. It appears to be a sort of job-sharing, except that both of them work full-time.
I don't know either of them personally, and I don't have any inside knowledge of that school. If they say it works for them, I'll take them at their word. But I don't buy the structure for one minute.
Deans are, among other things, supervisors. They give direction (sorta), allocate resources, and evaluate faculty and staff. Doing that well requires a level of consistency that can challenge a smart and thoughtful person. Ensuring that two smart and thoughtful people are that consistent both individually and together is a remarkably labor-intensive and fragile undertaking. Even in the best case, it's the sort of thing that works until it very much doesn't.
That's not unique to deans, either. I'm no fan of long term co-directors, co-chairs, or even "dotted line" reporting relationships. If you have two bosses and they aren't in sync, how do you know what to prioritize? As one of two supervisors, what do you do if your estimate of someone's performance is significantly different than your counterpart's? The potential for political shenanigans -- intended or accidental -- is too high. And all of the intensive extra communication required to prevent disaster amounts to a deadweight cost.
These objections don't necessarily apply to ad hoc teams for short term projects. Team teaching can work, for instance, and co-chairs are the norm for institutional self-study teams. But in both cases, two major criteria hold. It's a project, rather than a full-time job, and it's time-bound. The semester ends, the report gets written. Under those conditions, the downsides of power sharing may be worth the gain. But on an open ended, full time basis? No.
Finally, of course, there's the financial argument. Paying two deans to do one job is a waste of scarce resources. I'm not usually a fan of "administrative bloat" arguments, but in this case, I'd have to concede the point.
My fearless prediction, guaranteed or your money back: this won't catch on. It's a disaster waiting to happen, and an expensive disaster at that. No, thanks.