There's not very much empirical evidence that supports that. It's definitely true that when people have high deductibles, they spend less on health care. What is not at all clear whether they spend more wisely. So consumers don't seem to choose as wisely in the health care world as they do in the supermarket. Some of the apparently obvious solutions like high deductibles and health savings accounts are not perfect.
Economist Ed Dolan of the Niskanen Center talks about employer-based health insurance with EconTalk host Russ Roberts. Dolan discusses how unusual it is relative to other countries that so many Americans get their health insurance through their employer and the implications of that phenomenon for the structure of the health insurance market. Dolan explores the drawbacks of this structure and makes the case for what he calls Universal Catastrophic Coverage.