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.)

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.)

I question the assumption about immunity. Something that never goes away is very different to an exceptional event. The flu is never leaving us because we would need a universal vaccine that was administered at birth for the entire human population (animal reservoirs for coronaviruses are many). We don't have 8 billion doses of any vaccine, let alone one that works universally and for sufficient duration, and we don't have the infrastructure to reach everyone anyway. 

There are lots of reasons not to complain. If your life has already been destroyed there's nothing to go back to. People in ruin have other things that are more important than getting on twitter to bitch. Much damage has already been done, everyone knows that nobody responsible will ever pay for that. Everyone knows that plenty will never recover. Everyone knows that ultimately nobody cares, and that the second this is out of the public (and especially political, not that they aren't milking it for all its worth) consciousness it will be nothing more than a footnote.

Secondly, given the filter bubbles we all live in the odds are that there's plenty of complaint that you are never exposed to. The majority of my trusted media and commentary sources have been complaining since the beginning (The Mostly peaceful protest meme springs to mind as an example of the severe disconnect that the tribes have with each other). So from my perspective this exists, and you either aren't exposed to it or you see it and dismiss it (like we all do). This isn't across your media because your media is heavily filtered and biased (like all media is). 

Getting a clear picture these days is a lot of work, and that's something a lot of people don't want to do - and that's before they start redpilling and blackpilling themselves with whatever they dig up. I know that the more I find out about what's happening in the world the more disgusted and demoralised I get. All news is inherently biased against whitepills, and so is our very biology. We evolved to pay more attention to threat.

Immunity certificates are the kind of thing that those that favour authoritarianism want. Anyone with half a brain can see what a disaster that would be, but when people are a part of the group that is on top and enjoying punishing others they rarely stop to consider logical consequences (ie. make shackles, have them used on you). What can you do? There's no vaccine for stupidity and there never will be.