This is a good point. It drastically increases my estimate probability of your hypothesis being correct.
I would have guessed that the primary reason why the placebo effect has gotten stronger is that people believe in medicine more. There have been studies that show a stronger placebo effect if things feel more medical, such as making the sugar pills not taste good or the like. This suggests that the belief level can be quite malleable. But this now makes me extremely interested in your hypothesis.
The placebo effect (benefit in groups receiving fake pills) and nocebo effect (detriment in those same groups) have frequently been the bane of medical research. They are usually explained in terms of psychology: because people receiving placebos believe they have been treated, they get psychosomatic effects that cure symptoms and create side effects. This explanation is supported by the fact that the placebo effect is strongest when the effect being studied is subjective - eg, tests of painkillers and antidepressants. This explanation is neat, tidy, and in my opinion, altogether unsatisfying.
I have an alternative theory. Most people in medical studies take more than one medication; in addition to the drug being studied, they take unrelated drugs and supplements, usually including a multivitamin and often including other things they were prescribed. However, many people take their pills inconsistently; they miss or mistime some fraction of their doses. This is especially true of depressed people. Prescribing a placebo, however, fixes this; when they take their placebo pill in the morning, they are reminded to take everything else they should be taking. In addition to making pill-taking more salient, being prescribed a placebo may also cause some people to fix the organization and affordances they have for taking pills.
I suspect that many of the benefits attributed from placebos may in fact be due to increased compliance with unrelated prescriptions and correction of vitamin and mineral deficiencies. Arranging a study to test this should be fairly straightforward; simply measure the rate at which unrelated prescriptions are refilled in two groups, one of which receives sugar pills and one of which does not.