@mathdoc you have presented clear arguments for how you wish to raise your child - to respect authority, to obey rules, to seek to change them where necessary, but until that change can be effected, to continue to obey.
However, your post asked whether you were being unreasonable to expect others to help validate the choices you have made in raising your child, and to save you from having to present your arguments to your child and to stick to your principles in the face of obvious different opinions from others.
In that you are entirely unreasonable.
Some parents prefer to teach their children that when a law is not only irrational, it is detrimental to the well-being of the entire community, it is okay not only to question it, but to break it.
This country has a proud history of civil disobedience. Some of us prefer to teach our children that sometimes civil disobedience is the only rational response to a government that isn’t listening.
You went on to be unreasonable in attempting the argue that your position of not allowing your child to play in playgrounds was based on an actual risk, therefore also objectively validating your position as saving lives. You made a batch of hand-waving calculations, based on assumptions none of which are proven, and some of which have never even been postulated by scientists, epidemiologists, medical practitioners or even the WHO, and came up with a number of 3 extra deaths by opening playgrounds (not early, but presumably at all).
Even accepting your number (which I do not), it is worth considering the extra deaths that have undoubtedly occurred through domestic violence because of the lockdown. Could some of them have been avoided if kids and parents had had somewhere to go and play? I don’t know, and neither do you. What about the deaths that may result from increase in childhood obesity because there was nowhere for children to play? What about the deaths from mental illness and depression in children - there is clear evidence that the lockdown has contributed to that. Using your own numbers, maybe closing playgrounds only contributed to 0.0001% of those extra deaths...maybe the extra deaths from the lockdown were only 2% (actually the evidence is that extra deaths from all causes due to lockdown will be many factors higher than 2% of the total.). I think you understand my point... Lots of handwaving calculations are possible...
The degree to which the welfare of children has been disregarded throughout the pandemic response is a public disgrace.