A breakdown scenario in a rural area could mean 1000s of wasted doses
Don't you think Western countries are ordering many thousands more doses than they actually need?
Breakdowns happen - places don't need to have perfect infrastructure in order to warrant treatment.
Once the world is open the US and UK will be happy to say that they were able to cancel some unused vaccine supply if it turns out not needed. (which will be easy - between focusing on poor countries and moving production to something else (or winding down) as they recognize the need is gone they will be willing to end those contracts not completely filled. Politically it is a money saving move.
Of course the above assumes best (or at least) case. There are many ways things can go wrong. If all approved vaccines need a booster every 6 months things will be very different. (this is an unlikely but still possible very worst case)
They should be able to put out a general announcement and get thousands to get the vaccine if they need to. A lot of people who can get off work on short notice if there is an emergency. Obviously not everyone, but thousands can be redirected to someone else on short notice. Of course this requires emergency shipments to those who should have got the original, but the breakdown would require that anyway.
I don't know what the thawing protocol is though - this is a real concern that needs to be handled. I assume those who deal with the logistics have plans and backup plans that account for all of the above.