I think the main function of the vaccine in the initial stage is to lower the amount of people who need hospitalisation after contracting covid. So giving limited doses to the people who are most likeley to develop severe symptoms seems like best strategy to achieve that. Even if it pushes back date of achieving herd immunity a little.

So prioritizing health care workers (they can easily contract and spread) and old people (a lot of them need hospitalisation) seems like a good idea.