I was Unschooled, which is an interesting way of teaching children by letting them first de-stress from school, and secondly letting them develop learning naturally through curiosity. Anyone who is the parent of unschooled children will tell you, that there's a period of up to two years at the start where you have to account for the fact that the child will most likely do... nothing. Just game and not pursue any learning.
This is a period of time where the child is both de-stressing, and learning how to claim the task of structuring and scheduling for themselves, and is one of the most vital parts of unschooling.
What you find as a result, is that myself and many of my peers would then go off and seek out learning and structure our own days by what we wanted to focus on, whereas many of my schooled friends were incapable of working or performing any sort of task outside of that structure, and were overall too stressed out to be able to approach doing tasks in a positive way.
I think that this is what has happened here. Many people in America and the UK spend their entire lives being told what to do at any given moment. They are thrust into school at a very, very early age, and from that moment they are given tasks, kept occupied, never allowed time for self-reflection or allowed the chance to develop insight into themselves as people.
By the time they reach college and later university, they end up "going off the rails" a little bit during summer breaks, because they are suddenly, broadly, not told what to do within those periods. Academia still has the scheduling that school does so they are still safe within that system within those months and hours that are accounted for, but this scheduleless existence becomes a form of stress for them, because they have never developed those vital skills.
Then finally, they are thrust into work, where many will have a schedule to adhere to, within which they essentially, broadly, stay for their entire lives.
I don't think that your sister's inability to perform her hobbies when she was outside of a structured environment was a positive effect of the aforementioned institutional structures. I think it was a function of stress and a lifetime of her being prevented from developing the skill of having control over large groups of unbounded time. Your sister was not used to having a lack of structure, not used to other people not having some degree of control over her life, and in conjunction with that she very likely had a lifetime of accumulated stress that needs to be chafed off or worked through before development of that skill can take place.
What you saw wasn't your sister failing to perform her hobbies, it was your sister unknowingly de-stressing and gradually learning the skill that she had been deprived of learning. The fact that this of itself creates a lesser form of stress as a second order effect is deeply unfortunate.
This is absolutely, unequivocally, not a positive benefit of institutions. The fact that broad swathes of institutions have created people that are unable to function without them, unable to find meaning in their lives, is a severe indictment of them. It very clearly outlines how successful the Prussian upper classes were in creating a system where their workforce was essentially, psychologically 'neutered' in some sense, and pushed to become completely dependent on them for meaning. In essence, they created one of the best institutional tools to create a mostly-compliant workforce. A swathe of people who are unable to attain meaning in their lives and fulfill their personal goals outside of the structure of work in service to the economy and thereby the upper classes.
Do not take this as a recommendation for Unschooling in general. I (broadly speaking) do not wish all children to be unschooled, since it is highly environmentally dependent -- not everyone would be able to sustain the environment required, whether through the psychological issues of the parents or other adults in the vicinity, deficits in the environment itself, or specific psychological needs of the child.
There essentially isn't a solution to this right now, that I can see. Given that the Prussian success has been so great that many people cannot even start to conceive of alternative systems in the first place.