This grew out of a discussion of bedtimes and if it was necessarily "radical" to eschew them.
Certainly people have different needs. At the same time, it's easy to mistake cultural assumptions for "needs" - or use cultural assumptions to conflate several needs into one "solution". When that solution doesn't work, then it makes good sense to pick those needs apart so you can find ways to meet them separately.
One very common modern cultural assumption is that parents need time away from children. One of the assumptions layered into that one is a dismissal of the needs that parenting actually fulfills. When you recognize that engaging with your kids meets Some of your needs as a parent, that can help "fill you up" a bit more, so you're not riding so close to empty - which can help you delay gratification a bit longer on other needs for awhile.
Another hugely common modern cultural assumption is that parents get their grown-up needs met after kids go to sleep - all of them: privacy, adult conversation, intimacy, rest, and sex. That's a Lot of pressure to put on family relationships - so if it's not working, it makes good sense to pick those needs apart and look for other ways to meet them. For a parent who works outside the home and needs actual solitude to transition from work to home, it can be really beneficial to look for ways to provide that - which could be a room in (or adjacent to) the home where that person can be undisturbed, or it could be going someplace else in between work and home.
I'm not saying anyone has to do any of those things, only that when rolling a whole bunch of assumptions into a ball doesn't work, that pulling them apart makes good sense
And to reiterate, there's nothing whatsoever wrong with gently helping someone you love find a rhythm that works for him or her. It's kind and sweet - and kindness, sweetness, gentleness and care are some of the basic tools of radical unschooling.
As a moderator, I'm really concerned with what I'm seeing as a need to "put unschooling in it's place" so I think it could help to articulate what unschooling is really about. Unschooling is derived from the assumption that people - including children - learn as a natural life process, and that learning cannot help but respond to an individual's (even a child's) feelings and perspectives. That's the root - the "radical" of unschooling. It's not anything particularly special. People learn, feelings matter, children are people.
What that means in terms of something like "should I put my kid to bed?" is that Your Child's Feelings will have a direct effect on what he or she learns from the process. If s/he feels small and helpless when you do that, then s/he'll learn things about helplessness. If s/he feels supported and cared for, s/he'll learn about care and grace. What you choose to do, then is less important than how your child feels and what s/he thinks of you as a result of those feelings.
That extends to the issue of "alone time" for parents, too - if mom and dad wanting to be alone feels exclusionary and hurts a child's feelings, that child will learn something different than a child who has a different perspective. You can't control that perspective - but you can observe and choose how to respond. It's Okay to be sweet and kind and supportive when that's what helps your kid feel good about life.
Going back to the original question, about "the "radical" aspect" - the problem seems to be that mom and dad were applying a set of expectations and those expectations did not work out. That was not any kind of unschooling, radical or otherwise. It was just a mistake - and learning often depends upon mistakes. Mom and dad tried a different set of expectations and at least based on one criteria (getting enough sleep) that seems to be working. The problem, from an unschooling perspective, is that it's not clear how the child feels about that - and feelings, even the feelings of children, matter Because they directly inform what a person learns.
If your goal is to learn more about unschooling, then the thing to do would be to take those feelings into very careful consideration - which isn't the same as automatically saying "this doesn't work" if the child's feelings are hurt! It might mean acknowledging that parts of the routine don't serve the function intended and looking for ways to modify things. It could mean commiserating - saying "I'm really sorry, I don't have a better idea right now" or something of that sort. If his feelings aren't hurt, if he feels sweetly supported, then great - you found something that seems to be helpful for your family right now. That's lovely. And it's much more like "radical unschooling" than expecting a little child to figure out the complexities of body energy management independently. But again, it's not about the "what" so much as way feelings intersect with learning.