What I think it should have taught people, but probably didn't, is that vaccines for any pathogen that might be a pandemic or endemic in the future needs to have preservatives, and be designed for use in multi-dose vials. Not having preservatives in the US authorized COVID-19 vaccines directly caused them to only have a few-hour shelf life after being opened, and it also limited the number of doses per vial, as every violation of the stopper (really a synthetic rubber diaphragm, but it's called a stopper) increases the chance of pathogenic bacteria entering the vial. Obviously mRNA vaccines are more fragile, but an open, partially used vial that includes preservatives can last for years at a totally usable and approved state in a standard refrigerator. See eIPV ("IPOL"), authorized for use in the US for an example. From the WHO, some potential pandemic or large scale epidemic viruses are: Crimean-congo Hermorrhagic fever virus, Highly pathogenic emerging coronaviruses relevant to humans, Rift Valley fever virus, Nipah virus, Lassa fever virus, Ebola virus, and Marburg virus. For the last two at least, there are multiple strains, and I would be careful about saying "we have a vaccine for Ebola", for example, as there are multiple strains of Ebola and the US vaccine probably only works on one or two.
TLDR/in conclusion: put preservatives in your pandemic/epidemic vaccines. Supply chains fail, don't rely on the idea of single dose vials or prefilled syringes.