If you have access to statistics for the general population, you can forego the control group, I would think. But that requires doing the study in a country with a well run health care system and properly regulated medical records so that you can get these stats without privacy issues.
You can also use Canada, with the exception of access to medical records, to minimize all of the differences between populations in the USA and the control group.
Denmark has a very different vaccination schedule because they have exposure to many fewer "childhood diseases." Might seem like a small difference given the availability of 'properly regulate medical records without privacy issues" but these sorts of differences add up.
(Glances in Denmark's general direction.. )