I think that things would be approximately the same.
The government [in]competence is a result of how the entire system works, what are the individual incentives, etc. The entire system would start in the same position.
Looking at historical examples, no matter how serious the disease, many people always believed that vaccination was just government's secret plot to murder them. So even assuming that people would care more if it was mostly about kids... we would get some people more hysterically pro-vaccine, and other people more hysterically anti-vaccine. Social networks would be full of pictures of disfigured and/or dead children, but some people would claim they were killed by the disease, and other people would claim they were killed by the vaccine, and these groups would block each other.
In our universe, the most vulnerable people are the ones who vote most often. In the alternate universe, the most vulnerable have the least power. So I doubt they would have done much better in terms of real results. I do think there's more social pressure to care for children than for the elderly, but that may have only resulted in more effort wasted on measures that show off our devotion to those values without actually being effective.
"I would dare to say that the pandemic could be over by now." Then you need to learn more about pandemics. The point of a lockdown isn't to end a pandemic, the point is to buy time. There are only 3 ways pandemics "end". Viruses need their hosts, so most often pandemics "end" when viruses mutate to become less deadly. Modern medicine has also let vaccines be an alternative way to reduce virus fatalities to acceptable levels. Lastly, there's natural selection and only people who have natural immunity survive, but no one wants that.
A more severe and diligent lockdown wouldn't have accelerated vaccine development, and it wouldn't have removed the virus from existing, but it would have actually slowed the mutation of the virus. I don't know what flawed logic you are using to lead you to believe that a more authoritarian lockdown could have ended the pandemic early.
It's also bad logic to assume a virus that targeted children would have been handled less divisively. Do you remember before Covid-19? Anti-vax parents kept losing kids and it wasn't changing their minds. We live in a world of disinformation. If Covid targeted kids, anti-vax people would be fear mongering that the government and vaccines are killing kids.
You seem to think the problem is that the people "in-charge" didn't have enough power and authority. Look at China, you would think their authoritarian system would actually be good in pandemic situations because they could just blockade entire cities in and whatnot... But China instead cared more about prestige and in the early days of Covid tried to make people believe the virus didn't even exist. This is another reason why your line of thinking is detached from reality. You think giving more power to the people in charge would solve your problems ignoring the possibility that it isn't the system that's flawed but instead the components. Let's not forget who the US president at the time of the outbreak. You really think harsher action from politicians would have lead to a better outcome?
At the beginning of the pandemic, I was unable to predict how utterly incompetent most Western governments were going to be to handle the situation at all levels (barring some honourable exceptions) and I have had to update more than once my model of how inefficient the political structures are to handle crises like this one. Have I updated enough my model? I am not sure. I am barely surprised with any new intervention they announce, mostly because in my (updated) model of the world, we live in a deeply inadequate system where the people in charge are not really trying to minimize the damage of COVID.
Imagine an alternative universe where the virus affects mainly children, i.e. the younger someone is, the higher the risk. About 10% of newborns getting COVID will die. It still might affect adults but it is way less likely. Old people are mostly asymptomatic. My question is, how different would have been a world like this? Would have we seen the same amount of controversy around the vaccines, mask mandates, etc? There is a part of me that believes that politicians would have taken way harsher measures to nip it in the bud, that the bureaucracy would have been forced to evolve faster than the virus and that we would have not seen the same polarization we have seen regarding lockdowns or any other intervention. I would dare to say that the pandemic could be over by now. However, at the same time, I am thinking that I might not have updated enough my model of the world and the system we live in is so absolutely disastrous that not even a situation like this would have forced society into a better Nash equilibrium.