Time for a re-post:
One of the problems is that they will potentially save you from minor injuries such as grazes and bruising, without doing much (or anything) about the deceleration of the brain that can result in far more significant injury.
This is indeed a problem that has been found to occur with head guards in martial arts / boxing etc, which were introduced at the behest of the medical profession to reduce/prevent head injuries (after all, it's 'common sense' that they must, right?). It is now accepted in medical circles that these have increased the frequency of brain trauma which remains undetected and untreated, because the tell-tale signs of bruising and cuts (which would have otherwise stopped people from training / competing until healed) are no longer present.
If your head hits the ground and bleeds, you are quite likely to consider the possibility of brain trauma and do something about it. Medical professionals are quite likely to take the possibility seriously too.
Hit your helmet on the ground and consequently don't get a grazed head: Will you or the medical professionals treat as for concussion - and the potential for worse? You and they should, but there is a risk that this won't happen.
For those about to question (again) how this is relevant to cycling (where you don't have someone deliberately banging your head, read the italicised sections.