That's not a counterpoint, that is exactly the point. Maybe it becomes clearer if you read the speech. Math is hard, but it's being made much, much harder than it has to be.
On the one hand, academia has become rather harsh and intimidating and there is room for all kinds of improvement.
On the other hand... there is no world where whoever just wants to study math can just go study whatever they want for as long as they want, regardless of how well they do it. Of course, when I spell it out, that probably seems obvious, but I suspect this may be the unexamined assumption in a lot of people's heads.
Plus I suspect you missed my "regardless of how well they do it" clause. I doubt that you can flunk every math class over and over and just keep attending. Loopholes that big get noticed, exploited, and closed very quickly.
In recent times, the pressure to finish or drop out has increased, and studies have become more rigorously structured (or infantilised...), particularly with the introduction of the Bachelor/Master system.
"There is really no point in doing any exercise unless you're aiming for Olympics level performance. Yes, it's somewhat harsh and intimidating. But there is no world where whoever just wants to can just go do sports and exercise what they want as long as they want, regardless of how well they do it."
I think that was the point of the article - doing maths as a way of life (like exercise), not just for your career with the aspiration of being the best.
I'm speaking in a context where we're talking about academic life and academic life being harder than it needs to be. I think that's the only way to read this context, because nobody is making self-study "harder than it needs to be", so reading this thread as being about "life in general" doesn't make any sense to me.
I think the article is precisely not about professional mathematicians in academia. To quote: "If mathematics is a medium for human flourishing, it stands to reason that everyone should have a chance to participate in it." (my emphasis).
I solve Project Euler problems for fun. The article presents an argument that more people should do something similar, and more mathematicians and maths teachers should support it.
Certainly in Sweden, once you're in, you're basically free to hang around at University and study for as long as you want. It's not like they're going to kick you off campus.