So Teleology, you propose.....
"Ready, shoot, aim?"
You need data to know where the costs savings opportunities could be.  You also measure results using data.  
I hardly think that higher costs are due to an overabundance of data, given total administrative costs of 2.5% (not chump change I agree).  It would seem logical that you should go after the low-hanging fruit first, like opportunities to reduce hospital costs, pharmaceuticals, and doctor costs (which together exceed admin costs by 25 times).  Smart use of data is important.
I know in our research field and my related business, the availability of data is light years ahead of where we were even 10-15 years ago.  This has greatly reduced costs throughout my business and for our competitors, and clients get far more product for the same price today.  Why?  Better data, better technology, better information.  Health care is an assembly line, not as uniform, but to treat millions of people each year, you need systems and admin.