While I offer no opinion about whether vaccinations should be compulsory, it must be stated that if they should, it certainly isn't because of your argument about pure democracy. In a pure democracy, 90% of the population can choose to oppress the other 10%, and they have, many, many times throughout history.

If vaccinations should be made mandatory in a free society, it is solely due to the externality imposed by the unvaccinated on others (like you mentioned with ICU capacity, as well as general pathogen propagation), and avoiding that violation of the broader public's freedoms.