Well, just looking through a number of news articles over the past couple years to see what the issues were, it looks like it effectively comes down to too many cooks in the kitchen.

It's not like insulin, where the creators sold the patent to a university for everyone to be able to use anywhere in the world. The Covid vaccines has multiple companies and multiple countries all having an interest in the product. Add in that a company can patent one part of the system that could render the rest of it useless. For instance, I use Flonase Sensimist, which is now over-the-counter. However, it doesn't have any generics because Glaxxo-Smith-Kline patented the delivery system, so anyone coming out with a generic would have to come up with a new delivery system. (This also was an issue during the whole Epipen debacle and the competing company had to come up with a different delivery system from what epipen's system is). If you have a vaccine, but can't delivery it to the person because you can't get the delivery system, it's essentially worthless.

I'm not saying it's right or wrong or whatever (I, for one, would love having a generic of Sensimist to use), just that's basically the answer to your questions. Too many cooks and the ability to patent pieces of the full package.