Dr. Fauci hits back on the idea that the process was rushed or that safety was compromised. He was talking yesterday about technical advances that sped up the process this time. Also, pharma companies have been producing vaccines "at risk," which means producing them before approval so they're ready to go if the OK comes. If. They could also lose tons of money using this approach.
Remember that back in the early days (March maybe?), Dr. Fauci said vaccines take a long time to produce but that we could have one by January. So we're really pretty much on the normal schedule he envisioned.
Finally, the reason vaccines aren't being distributed right now is that they're waiting for enough time to pass to be sure there won't be serious side effects in a 60-day window.