A case can be made that balanced response -- that is, achieving similar response rates across all the subgroups that can be defined using sampling frame and paradata -- will improve the quality of survey data. A paper that I was co-author on used simulation with real survey data to show that actions that improved the balance of response usually led to reduced bias in adjusted estimates. I believe the case is an empirical one. We need more studies to speak more generally about how and when this might be true.
On the other hand, I worry that studies that seek balance by reducing response rates (for high-responding groups) might create some issues. I see two types of problems. First, low response rates are generally easier to achieve. It takes skills and effort to achieve high response rates. The ability to obtain high response rates, like any muscle, might be lost if it is not used. Second, if these studies justify the lower response rate by saying that estimates are not significantly changed by the lower response rate, then they run the risk of moving down a slippery slope.
Think of a hypothetical 10-call data collection protocol. The first step toward balance might be to reduce some groups to a 9-call protocol. They find that the 10- and 9-call protocols are not significantly different. In the next step, they compare the 8- and 9-call protocols and decide that they are not significantly different. And then 7 to 8... and so on... None of these steps are large. But the difference between 1- and 10-call might be significant.
Finally, as in this last example, obtaining high response rates on at least some surveys or some subsample within a survey provide a means for evaluating the risk of nonresponse bias on other surveys or the rest of the sample.