A few years ago, I was presenting at a conference of substantive experts. I gave an update on a progress on a survey of interest to this group. I talked about how nonresponse bias can be complex, and that the response rate might not be a good predictor of when this bias occurs -- based on Groves and Peytcheva. I was speaking with one of the researchers after my presentation, and I was surprised to hear her say that she interpreted my comments to mean that "response rates don't matter." Although that interpretation makes sense, it hadn't really occurred to me in that way until she said it.
Since then, it seems like we've seen a lot of published papers and conference presentation where lowering the response rate becomes a tactic for improving the survey. Most studies taking this tactic lower the response rates for groups that tend to respond at higher rates. The purported benefit is response set balance on known characteristics from the sampling frame is improved. Some other studies show that lower response rates don't change estimates. A side benefit is that costs go down. One paper that I know of does have some validation data to show that nonresponse-adjusted estimates actually would have reduced bias with a strategy that lowered overall response rates in order to have more balanced response rates across subgroups.
There is some logic to this approach, But, I worry that lowering response rates might be a long-run bad policy. First, there is a minimum response rate, so this strategy can only work for so long. Second, once we lower response rates, we lose the ability to track what higher response rates might be getting. If a study has validation data, this might not be so bad, but for other studies, it means we won't have the necessary data for considering cost and error tradeoffs. Third, and this is a problem for the field that no particular study may want to address, but once we lower response rates, we lose the ability to obtain higher response rates. We won't know how to do it. So, despite the lack of a clear relationship with bias, there may still be reasons to maintain or (for the audacious) even increase response rates.