@Foxi4 already outlined the dangers of rushing.
He/she did not.
In the Cutter incident, the company in question - as well as all companies at the time, had a problem with killing the polio virus they would use in their vaccine. This was known internally in one case, where they discarded batches, but didnt report it. This was before liability laws were installed that prevent companies from doing that without being legally liable. This was a manufacturing issue, not a vaccine creation issue. This had nothing to do with development being rushed. This would be prevented today by the mere fact, that nowadays you only have half a dozen of manufacturers, that can produce vaccines at scale (and they still want to be in business 10 years from now). This would be prevented today by the mere fact, that we aren just sticking dead Covid in a tube with the development of this vaccine - we are basically isolating part of its RNA and splicing it into a carrier virus, or modifying another virus in a way that antibodies would be produced that would also work for Covid. Or just manufacture the entire thing, but make sure to leave the parts out, that make it a living organism.
If you entirely make up your reality - why make it an effing dystopia. If you are too lazy to read, again - dont participate.
But once available, it should be really available to everyone. I won't speak on behalf of the US for civil reasons, but it should be obligated at to the groups where it's safe to do so.
Again if you had read the articles already posted, you wouldnt have to make wishes to the universe. You would already know, that people in deciding positions already know that leaving out parts of the world is a bad idea as the virus can start propagating from there again. At the same time, nations payed sometimes for 6x the needed dosis to be produced by different manufacturers, just to get a working vaccine as soon as possible, when ready (after clinical testing finished), and they did so to minimize economic damage to their economies. The US - by far - bought up the most capacity. Efforts to finance vaccine development/production entities for poorer nations largely failed so far, but there are pledges, to allocate capacity to poorer countries and donate (this ensures, that economic gains remain in western countries). Largest vaccine manufacturer by volume also is situated in India. Efforts to open up and share intellectual property, werent met with too much enthusiasm on part of the rights holders, so that isnt happening to a large extent.
As far as distribution in western countries is concerned, medical personal is first, then come older people, and by virtue of them paying more, probably international business travelers. At least in countries with a national health system (that still allow private parties to pay more to fasttrack their 'position in line'). All of that is already decided. But then governments with national health systems currently are buying up capacity 'for their entire countries'.