There are unfortunate life circumstance that falls upon you. These do exist and I would also definitely be more flexible to help someone undergoing them. Your child is not an unfortunate life circumstance. He is the consequence of a choice you made. Just like my schedule is the consequences of choices that I made. There is no reason to consider that your choices matter more than mine.
The only relevant "choice" here is the choice that companies made to close their offices and require employees to work from home. For people with children in their homes that is going to mean they are less productive, even if there is a babysitter available. If your company told you that you are required to do your work while riding on a roller coaster, where you would likely be much less productive, you would be right to ask the company for to reduce your expectations until you are allowed to return to your office. Since parents are being required to work from an environment where their productivity will be lowered, it is reasonable and everyone should expect that their expectations will be adjusted downward to reflect that. If your home environment does not significantly reduce your productivity then there is no reason to think your own expectations should be adjusted downward.
You would be exploiting a system put in place to help families survive a pandemic for your own personal gain.
I'm with you though. If I have personal obligations, I shouldn't feel any pressure to help out a coworker by working later than normal with no additional incentive just because they have children and I don't. And if I decline to help out that coworker, I shouldn't be publicly shamed.
The child rearing consume what the childless have earned under the "do what's best for everyone" motif of social programs. Who's getting the best? Do the childless get to participate in this best?
I really don't understand how you can have a perspective that leads to this question.
This was always OK before the pandemic. Everyone stopped working at 5, and I got to get ready for my hobby at 6. All good.
Now, parents need to be available for their children at 5. So they have to leave at 4. Someone has to stay until 6 to "make it up". It's a priority that we allow them to be available for their children. So I will have to let go of my hobby, so they can be with their children.
They might even justify it by saying "I will come early on thursdays to compensate, and you can start later". The thing is that I don't care about starting later on thrusdays. I want to be free at 6 on wednesdays.
And because my calendar does not include the magic "children" word, I automatically get the lowest priority when discussing schedules. Holidays during thanksgiving ? No sir, you don't have children, you would probably be sad and alone anyway! Those nice summer days ? Well, Henry wants to take his gasp children hiking during summer break, you can have a week in november, while his son is at school! And so on...
The children word is systematically used as an argument to justify some kind of priority for parents when defining schedules over those who don't have any children. And COVID made that really visible because people with children suddenly had even more constraint than those without - and you can guess who had to be even more flexible. And because non-parents are systematically being shown that they matter less, this creates resentment.