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.