I think people who are immune are often either 1) risk-averse enough not to change their behavior or 2) responding by changing their own choices rather than pushing for changes to government restrictions. I think your surprise is coming from over-estimating the extent to which people's behavior is driven by government rules.
The difference between my behavior currently and my probable behavior post-vaccine or post-infection would be almost entirely about changing self-imposed restrictions. I could already legally eat in restaurants outdoors, work in restaurants, go to outdoor bars, see my friends in groups of <25, shop, go to the gym, get my hair cut, or travel by plane. To the extent I don't do those things, it's my choice, not a restriction imposed by the government. (The only thing I cannot legally do that I would like to do is eat in restaurants indoors, and I expect that restriction to be lifted in a few weeks anyway. And if I really cared about eating indoors, I could just drive to the next county/state.)
Ah, you've made me realize that I haven't thought through the variability between cities and states. As someone living in California, I currently cannot: eat in restaurants (indoors or outdoors), go to bars (ditto), gather in groups outside my "household", or get my hair cut.
I think there's a lot of other-optimizing and social pressure intended in this. Even if one is in the minority of immune (or near-immune), most of the people you care about aren't, yet. And we all know there are significant numbers of fools "out there" who'll claim immunity even when they don't have it. If we normalize risky-seeming behavior for a significant fraction of the populace, we're likely to see a whole lot of impostors spreading the disease.
Also, reinfection is very rare, and the vaccine is quite effective, but neither is perfect protection. The only real answer is the combination of immunity and risk-avoidance that really makes it impossible to spread.
Both of these motives combine to make me prefer NOT to return to normal, even if I personally am no longer at high risk, until it's just no longer a newsworthy quantity of new infections.
This is very much a "gut reaction" type answer to your question.
The ones that are most likely to be complaining already are -- and they don't care if they have immunity or not.
Those the do care probably see two down-sides to the "complain to get more normality". First, they will tend to come across a bit as uncaring/snobbis: "I'm good now so you guys suffer on your own." or that that would be associated with the first group. (Given one can probably predict who someone voted for based on their being in the first group above that is really bad signalling.)
Additionally, who will they really be going out with at this point. Probably a bit of network effects here (going out is great, but not as a "solo" activity.) Plus, just organizing that movement will be problematic and activists have a number of high priorities at this time I suspect.
(Note, I am with you on that approach being rather reasonable and would love to see, at least a travel passport type exemption adopted -- have the proof of vaccination and international travel is now allowed largely as it was pre-pandemic, implemented.
Interestingly, I posted a comment here maybe a month back with the same type of approach. It was not welcomed as I recall.)
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As remizidae points out, most of these restrictions are not effectively enforced by governments, they are enforced by individuals and social groups. In California, certainly, the restaurants and bars thing is enforced mostly by the government, but that's mostly a "governments can't act with nuance" problem.
But for things like gatherings of friends, I think this question still applies. The government cannot effectively enforce limits on that, but your group of friends certainly can.
And I think in that context, this question remains. That is, I think groups of friends in California should start plans for how to handle social norms under partial immunity.
I have personally suggested this to friends a couple times, and I've met with a lack of enthusiasm. I think a part of that is that the question is so politically tribal, that taking any action that isn't MAXIMALLY SERIOUS is a betrayal of the tribe, even if it has no practical value.
Also, making any such plans public, versus just keeping a google doc of who among your friends has been vaccinated, creates a lot of social awkwardness, so I'd expect that in practice people will come up with their own personal, secret, and highly error-prone ways of handling it.
Assumption: COVID immunity lasts a long time, because that's how diseases work, and this is the case for 95+% of people who get COVID or a COVID vaccine.
20% of the United States has had COVID (13-30% per https://covid19-projections.com/) and presumed immune. Even if we conservatively take the official case count (20M) and trim off 25% to account for possible duplicates, that's 5% of the population.
Another 1-2% has already been vaccinated and will join them in a month, with more every week after that.
So on the low end, in mid-January, 7% of the country will be fine. COVID-fine, at any rate, but still subject to all local, statewide, and national restrictions.
Why aren't these people making noise about going back to their normal lives? They want to eat in restaurants and make money working in restaurants. They want to see their friends and shop. They want to do lots of things.
I notice that I am very surprised that this large and growing minority isn't insisting on partial re-openings (with immunity certificates?). I'm surprised they're not screaming for it. I'm surprised it's not a discussion all across the media. What am I missing?