I understand the good intentions behind your argument, but there’s an important point you haven’t considered: it’s not that some protection is better than none; it’s that there’s little evidence the first dose provides much protection beyond the first few weeks:
See this Scientific American article:
In the trials, the Pfizer vaccine provided partial immunity about two weeks after the first dose, with an efficacy of 82 percent. But there are no data on whether protection lasts longer than three weeks, when the second dose was given.
And this from the British Medical Journal:
Pfizer and BioNTech themselves have already urged caution on the grounds that their data ends at day 21, and “there is no data to demonstrate that protection after the first dose is sustained after 21 days”. It’s possible that the protection people seem to have will suddenly drop off after that point – in fact, this wouldn’t be surprising based on the way the immune system usually works.
[all bolding mine]
So we’re not talking about twice as many people having a pretty good level of immunity; we’re talking about the strong possibility that people having had only one dose will have very little immunity 4 weeks later, while that one dose is still being distributed.