In a lot of regards the "vaccine shortage" (hint: there is no real shortage, we are currently just in the early ramp up phase of production) should exaclty be treated like the toilet paper shortage.
Not really, because toilet paper was a different issue, there was plenty of supply. With vaccines I want the 300 million doses made in the US the day it is approved. Then nothing for three weeks and then make the booster all at once . That isn't possible, but it is what we want. (As each country approves repeat for them)
Note that even if a vaccine/drug/etc. gets approval, people are still looking for side effects. The approval process is designed to catch and document such side effects, but only once you give it to millions of people you find out about the side effects that are more rare. Also, due to the extremely sped up approval process, you know only little about any long term side effects.
Ideally you spread the doses over a few weeks or months so that you can stop the vaccinations should any issues arise. I'm not saying the current distribution is fine, it's far too slow. But not even Israel has vaccinated everyone in a single day, nor would that be a god idea.
This is btw also the way Google play distributes updates. Instead of every user getting the update right away, they first give it to a small group, then that group increases gradually in numbers.
A shortage is a is a mismatch between demand and supply. When you are in the ramp up of production, the art is to match these. That means a closely monitored planning covering both aspects. Which is exactly what was done with toilet paper.
Done right, one could even get away with not reserving the second shot from the first deliveries. Another parallel between toilet paper and vaccines is the sudden demand spikes, read additional orders from the EU in January, that resulted in reduced short term availablity.
