I feel like if the NHS started trying to hand out vaccinations for the common cold (or for the more common strains of it), regardless of how immensely impressed I would be with the researchers for puzzling that shit out, and regardless of how effective it was, I would refrain from being vaccinated. NHS is payed for by taxes (I know that a lot of countries don't have a national health service which works the same way) and I would rather those taxes are spent on building new hospitals and training new surgeons than buying needles to prevent a pretty harmless group of viruses which you recover from pretty rapidly on your own. But I guess that's not really relevant since we aren't talking about colds anymore.
And yeah maybe being able to isolate people who refuse vaccines in some way if they were suspected of carrying something dangerous could be a solution, just making sure they knew that they were putting other people at risk would probably be enough. I know this wouldn't be a complete solution to their detrimental effect on herd immunity but it could help a little with it. Although you are probably right that compulsory vaccines are an easier solution.