I don’t think this line of thinking really holds up. You haven’t pointed to anything a stay at home parent can give school age children that a full-time working parent can’t also provide outside school hours.
Plenty of full-time parents pick their kids up from school every day and parent them right through to bedtime. Flexible and hybrid working make this much more doable than it used to be. It’s not possible in every job, but employers are generally far more supportive of family life now than in the past.
After school, parenting usually means helping with homework, making dinner, driving to clubs or activities, etc. That’s exactly the same kind of parenting a stay at home parent would be doing during those hours. Evening chores like cooking, tidying up, getting organised for the next day etc exist either way.
I completely get that pre-school children need more constant daytime care. But once kids are at school, it’s simply not true to say full-time working parents can’t provide the same parenting after 3pm. Lots of families do this every single day.
That said, paid work and staying at home are clearly different kinds of responsibility, each with their own pressures. Being the main earner, dealing with deadlines, and answering to an employer isn’t the same as running a household full-time. And equally, caring all day for several children, especially with additional needs, isn’t comparable to going into an 9-5 office job. They’re just different roles with different stresses.
In the end, only each family can decide what works for them. The financial trade-offs are different too: a lower-paid worker staying home gives up something very different from a high-earning professional doing the same. That’s why broad comparisons don’t really make sense.