If the burden of proof is on the people who claim there's harm, and you prohibit funding of any further attempts to find such harm, that subverts the scientific process.
By this logic, the NIH should be funding endless studies of all kinds of quackery, such as putting magnets in your shoes to cure arthritis. There isn't unlimited tax money available to do unlimited numbers of studies on topics where no convincing positive evidence exists and there are strong, fundamental reasons to believe that the previous negative results were to be expected.
For a long time people suspected that electricity and magnetism were somehow related, but were unable to figure out how. How would things have turned out if those who believed they weren't related pointed to all the early failures and cited them as reason to cut off all funding for attempts to find a relationship between the two?
This is an apples-and-oranges comparison. In 1820, electricity and magnetism were not well understood at the fundamental level. In 2013, the interaction of nonionizing radiation with matter is well understood at the fundamental level, and has been for 150 years.
But those who claim there is a danger must be allowed to continue trying to prove their viewpoint. Otherwise you've turned science into one big circle jerk of confirmation bias.
I don't advocate prohibiting them from doing studies. I just advocate not continuing to give them tax money to do it, and not continuing to publish their inconclusive results, based on poor methods, in peer-reviewed journals. We don't fund people to continue testing the hypothesis that malaria is caused by bad air, or that maggots arise from decaying flesh by spontaneous generation. That doesn't make the germ theory of disease "one big circle jerk of confirmation bias."
Generally, the government agencies funding those types of studies do a pretty good job of it. They don't just keep funding the same study over and over. In order for the applicant to get funding, s/he has to propose something new and novel - either something which hasn't been studied before, or some way to conduct the study which hasn't been tried before and could give different insight.
What you're describing is the way it's supposed to work. Cell phones and cancer are an example where it doesn't actually work that way.