Contingency fees for doctors?

When I was an attorney in private practice, we were expected to take many cases on a contingency fee basis. This means that if we did not win the case, or make some sort of recovery, we did not get paid. When we did collect a judgement or a settlement for our client, we would get a percentage.

Recently, I went to the doctor and something a little abnormal appeared in a routine test result. The doctor insisted that several more tests needed to be run in order to determine what was causing the test to come back outside of normal parameters. End result? The doctor couldn't find anything and it was chalked up to my body just being "a little different". Soon after, I received a bill. Ouch!

Here is the question posed: Should society start insisting that if doctors want to run all sorts of tests to figure something out, before they bill us for their time going over these tests and making an assessment of the tests they recommended, should they agree not to accept a fee if it turns out that, in fact, nothing is really wrong? Should a doctor's fee be contingent upon the actual necessity of the tests the doctor recommends?