The issue is if you have someone with a scientific background doing politics, what you have at the end is still a politician. Same thing here. An MD doing hospital administration is an administrator.
Which is not to devalue specialist expertise in these roles. I definitely think you want people with these backgrounds in those roles as well. Just not necessarily exclusively. A career administrator has different skills than a physician, you want people with both, and other, roles working to run a hospital.
The real problem as I see it is probably the incentives, constraints, and pressures they work under, or towards. A physician forced to run a for-profit hospital maximizing returns is going to make a lot of the same decisions as someone with a business background in the same situation. The thing is to change the situation, not put different people into that role and expect them to do it dramatically better.