This is a double standard I notice in our society more widely.
The benefits of choosing not to work accrue entirely to that child and that family.
Yet the benefits of choosing to work are expected to be shared.
Firstly in tax taken from both parents salaries. They're sharing the output of their time working with the non-workers. At least 20% of the time that WOH parent works is taken in tax and funds state services which are equally enjoyed by the family with a SAH parent.
But the SAHP doesn't give a reciprocal 20% of their time to benefit the WOH family 
And then on top of that, as you say, it's somehow seen as wrong for the remainding (post-tax) WOH parent's salary to actually benefit exclusively their own child.... even though their salary is exactly what they get instead of the time the SAH parent puts exclusively into their own family!
It's not fair for anything to be available to the child of a WOH parent which isn't equally available to the child of a SAH/non-working parent.
But that only goes one way....
You even see it explicitly on this thread where pp say 'why should the children of SAH parents miss out, just because WOH parents can't make the event?'
Complete double standard.