[....] there seems to be at least some consensus that the main purpose of giving the vaccine now is to protect from serious illness or worse (which is BTW no doubt a worthy goal in its own right), how does that protect anyone else? You can still catch covid and transmit it, maybe slightly less than otherwise but still at a pretty good rate, so how does "everyone" being vaccinated protect everyone? And to take it a step further, what would be the rationale currently behind vax mandates if it mostly just protects the one taking the shot?
I’m not sure it’s helpful to think of it as a conflict between protecting myself vs protecting others. Rather, covid is a disease
of society and our overall goal is to decrease the amount of covid disease in society as a whole.
Of course, of all the people who make up a society, there’s one that I’m particularly partial to, and so I selfishly make a special effort to protect myself. But whether or not I get sick depends on two factors:
1. My own susceptibility to covid, and
2. How much virus is in the air around me.
I can try to decrease my own susceptibility to some extent by maintaining general health behaviors – eating nutritious food, avoiding obesity, getting a full night’s sleep, and also, to some extent, by getting vaccinated. When the vaccine was first brought out, it seemed that it would protect us against catching covid, but as a few months passed, it became clear that it wouldn’t go that far, but would prevent serious illness, hospitalization and death.
But the second factor that determines whether or not I get covid is how much virus I encounter, and that will depend on how many other people are carrying the virus. If I choose to isolate in my basement or hide out in the El Yunque rain forest, then I won't encounter anyone infected, and don’t even need the extra protection afforded by the vaccine. But if I’m going to move about in society, then I really want both – I want to maximize my own protection, and minimize the number of people around me who are potentially infected. I want to be healthy myself, but also to live in a society of healthy individuals.
When I get vaccinated, I contribute to both these goals – I give myself some added protection, decreasing the chances I’ll get sick, plus I decrease the chances that I’ll add to the amount of virus in society, thereby decreasing the chances that those around me will get sick.
The mandate, as I understand it, is geared mostly towards the second point, that is, trying to decrease the burden of covid disease in society as a whole. Its aim is not to paternalistically keep any one individual healthy, just like there’s no mandate to make sure you brush your teeth, much as we'd like you to do that. Rather it’s to keep society healthy, on two levels: First, to make sure that the number of sick individuals is not so great that it overwhelms the medical resources in our society (hospital and ICU beds, doctors and nurses’ time, drugs, etc). And second, to make sure that the number of virus-infected people who roam around our society are low enough to prevent large-scale transmission to others. As you note, even those who try to lower their susceptibility by getting the vaccine are not 100% protected, and still could become sick if they encounter enough virus. This is especially true for those over 60, who are about 20% of Americans. Also, there are many people who can’t get vaccinated, because they’re under 5 years old, or have some health condition that makes the vaccine dangerous or ineffective. So keeping society virus-free – or as close to that as we can realistically get – will help protect those people as well.
This protection offered by the vaccine extends not only to the physical health of those people who circulate in society, but also contributes to the economic health of society. An outbreak of covid has negative effects on schools, restaurants, shopping, entertainment, travel.
This is why the mandates were initially widely accepted by businesses. IIRC it was about 2 hours after Biden's announcement of the mandate that several large businesses announced that employees would have to vax. They clearly had thought this through beforehand, and welcomed the legal backing that allowed them to try to create an office environment that would minimize disease transmission to healthy workers, by ensuring that all their co-workers were vaccinated.