The math doesn't look too good, at least in the US.

There are currently about 100,000 vaccinations a day in the US. Ignoring the vaccines that need two doses, vaccinating 300 million people at that rate will take 3,000 days = 100 months = 8.3 years. At 1 million vaccinations/day, we're still looking at 300 days = 10 months. Logistics is not my thing, but a tenfold increase in vaccations may be a little optimistic. Better than an infinite wait, though.

I got a robocall from my regular pharmacy the other day, telling me that they would be involved in distributing covid vaccines "soon".

So I am definitely going along with the main idea about acting as if everyone I know (or run into on the street) has tested positive.