(If we did have enough doses ready to go for everyone, the government solution of "have the government buy it and distribute it to everyone" and the free market solution of "everyone and their insurance is very willing to buy one dose but values a second dose at $0" would basically collapse to the same thing, and so the author's argument would be moot.)
1A) healthcare workers (highest unavoidable exposure rate) & LTCF (highest mortality rate)
1B) frontline workers (high unavoidable exposure rate, and may be crucial transmission links) & the very old (high mortality rate). If the vaccine lowers transmission, we'll see a big effect from the frontline worker portion, which I suspect factored into the decision somewhat even if it is not acknowledged in the documents.
1C) This category is too big-- all essential workers and anyone with a health condition increasing risk or over age 65. This phase is actually bigger than 2. It needs to be split up some to prevent a mad rush for doses, and certainly we can benefit from further prioritization. Hopefully this is addressed, but it's tomorrow's problem.
2) The remaining group is smaller and probably the least interest in getting vaccinated, so I assume when we get to phase 2 we'll be facing different logistical concerns.
The really stupid thing we're doing, IMO, is reserving 55% of doses to ensure everyone gets dose 2. It should be a much smaller reserve (~25%): it's unlikely that Pfizer's production will stall entirely and even in that worst case scenario, most people would get a second dose, AND the data looks like 1 dose is likely effective.
This reserve is preventing many areas from having enough doses to enter phase 1B, and portions of phase 1B are parallel infrastructure (e.g. mass-vaccination clinics). So, allocating those additional doses could be expected to significantly increase throughput by activating other channels through which the vaccine is distributed.