I am dismissive because distribution is not big-H Hard. It consists of known unknowns and can "simply" be solved by application of money. Yes, actually it's a systems problem: there is not infinite money, there are political interests. But compared to the science the problems are well understood.
On the other hand we still have no idea how well these vaccines will work. First, we have (as I discussed) two different approaches in the three current candidates, one of which is fairly new and one which is completely novel. We have had only limited time to see how well they work and have only limited experience in broad efficacy, duration of effect, and, crucially, how long they last (it takes a long time to learn if you'll need a 10 year booster!). We don't know how fast the virus mutates away from the vaccine's target (though we do currently think we have a good idea). And we simply haven't tried enough people to get a good handle on side effects.
One of the difficulties in solving these is that new approaches contain unknown unknown. Look at CRISPR-CAS: got a (deserved) Nobel this year yet may already have been discovered to be ineffective or worse in the real world. That takes time to learn.
Now it's not that the people doing the work are idiots -- they know all these problems better than I do. But I am appalled that this is treated by the press as a distinction between, say, a pair of beta implementations of something, one in Python and one in Ruby.
Going back to systems issues: when we don't know these factors we take a calculated risk (really an estimated risk). The social aspects of vaccination (close to ubiquitous use, the risk of any side effects increasing the anti-vaxx rate for other immunizations, which itself could become a public health disaster etc) mean these factors are upmost in public health officials, not whether they have adequate refrigeration.
Vaccines are particularly difficult for reasons like these above -- there's a reason why they have their own special laws and government-assumed liability insurance. I haven't worked on vaccines, so take this as you will, but I have worked in anti-invectives, have designed preclinical and clinical protocols (including first-in-human) which were submitted and approved by the FDA, run clinical trials, have presented to the FDA and defended protocol design, so I have some idea what's involved and how to read the presented endpoints and findings.