So it's very important to follow the protocol here as much as possible until we know otherwise.
As for 3-4 weeks being too short, I'm not aware of any specific research there. But I'll assume you're right, and also tell you it's irrelevant: If a booster in 3-4 weeks improves efficacy, but doing it later would work even better, that does not mean we should wait longer: We still need the boost now. All your point means is that we should also do a second booster at some optimal time further down the road.
If you try to give the person a second dose, that means you're causing another person to be walking around completely unprotected.
Because if the vaccine wears off quickly. Then, the issue of the second person it moot. Vaccinating them becomes a net 0: Person A that got the first vaccine is losing their immunity while second person is gaining immunity.
However, assuming the pharmaceutical companies can & are massively ramping up production, and given that the logistics network for distributing & administering the shot is improving, We will hopefully get to the point when all of the above is completely irrelevant because there will be ample supply and ample bandwidth to administer the dosesto everyone.
I think in the short term we also get a little bit of a boost from the folks who have already been infected. AFAIK, their resistance may not last long-- as little as 6 months perhaps. But in terms of getting spread rates under control, and assuming twice as many people have been infected as the official record shows (which might be conservative, it's just educated guess) Then that means in addition to those getting vaccinated, We have about 55million formerly infected people that should have some level of resistance.
Anyway, thanks for an interesting conversation.
The question is whether or not they have verified it in this context.
Unless this virus is magically different from every other virus we create a vaccine for, waiting longer for the booster will create a better / longer-lasting immunity afterwards.