US gave 6 companies funding to manufacture polio vaccine in 1960s, 1 of them made it badly, Cutter laboratories they didn't properly kill the polio virus.
Result - out of 1.2 Lakh kids inoculated with live virus, 40k developed abortive polio, 200 paralysis, 10 were killed. https://twitter.com/scribe_prashant/status/1392010203650957314

It's takes years of expertise to manufacture a vaccine, which is safe and doesn't kill people. Asking people to make them at home, is like asking everybody make brahmos missile in their backyard, because didn't have money fund military.

Also unlike top secret brahmos missile, vaccine manufacturing formula are already public, when patents are filled.
So what's stopping the other from copying that. Well 1stly the patent itself, 2nd unlike generic tablets here u are dealing with live organisms,

have to prove that u can manufacture it safely and that takes time for clinical trials, else disasters like Cutter laboratories will everywhere and everytime.