I'm not even convinced that this would bring down total health costs, much less improve the "added health value" we get per healthcare dollar. The problem with covering catastrophic care, but not routine expenses is that you substantially distort health care economic decisions for the consumer.
Consider an individual striving to maximize their utility by adjusting their healthcare purchases as they try to decide whether to go in for a routine physical at the doctor. Now there are two main factors affecting their utility, the monetary cost of something, and the health outcome. In other words, getting advanced cancer is bad both because you get sick and possibly die and because the treatment costs money.
Now, there are good reasons to believe that the dollar value of health increases as one gets richer. After all, it's a lot easier to justify a $50k operation/medicine course if you're just giving up your fifth car than it is if you're giving up four years salary. And this effect should apply to pretty much all health-money trade-offs.
Now back to the matter at hand. For the rich, it probably doesn't really matter if routine medical care is covered, as they are willing to pay a lot of money for a single unit of health, so they will pretty much do more or less whatever gives them optimal health.
The poor make a more interesting case. They will tend to value money much higher relative to health than do the rich. Now in the fully insured case money will not be an issue, so they will behave in the same way as the rich. The fully uninsured case is also fairly uninteresting, they will attempt to maximize their utility for whatever health-money trade-off they have. In the limiting case, they will begin to go in for routine checkups only insofar as it prevents health expenditures later. (We assume here that individuals will do everything in their power to stay alive.)
Now suppose one of these individuals has a policy that covers only catastrophic care. Suddenly, the monetary loss associated with diseases such as cancer disappears (or is reduced depending on the specifics of the policy, it doesn't really matter). The point is that they will reduce their consumption of routine checkups, not only in comparision to the level which is associated with optimal health, but also the level which is associated with the minimum expected expenditure necessary to stay alive. These individuals will actually have increased total health expenditures compared to the fully insured case.
And this isn't just a hypothetical case, doing health screenings at local grocery stores, I've found plenty of people with blood sugars of 600 (meaning they had massively uncontrolled diabetes). Who didn't even know they had it. And these are people who DON'T have catastrophic insurance. If you give them only catastrophic insurance, economic incentives to be in that condition will only increase.