The fear is that doctors might reserve vaccine doses for family, friends, or highest bidders. The optics of such a situation would be terrible and would surely be in the headlines for months, but the actual odds of this happening and the resulting impacting are very low.
This follows earlier attempts by the CDC to optimize vaccine distribution according to racial demographics rather than which demographic was most susceptible to COVID (elderly). They eventually relented, but I'm still stunned that our own CDC was considering going against their own fatality models in an effort to appease social justice concerns. (Source: https://www.latimes.com/science/story/2020-12-30/how-race-fa... )
We had nearly a year to prepare for this situation. It's almost criminal that the government didn't think to prepare a vaccine distribution system that would have solved these issues well in advance. No doctors should have to scramble to find patients to accept a vaccine when under 10% of the country is vaccinated.