That would be fine if the quote didn't include this bit:

"...and their improvement is made to depend on allocating more resources to the management of hospitals, schools, and other agencies in question."

That's where he veers into making a policy recommendation (defunding social institutions), and where he is no longer engaging in critical theory but in pushing a particular policy agenda, therefore opening his critique (some of which I'd even agree with) to practical criticism from people with more skin in the game.

Critique is not helpful if you don't know anything about the feasibility of alternative approaches. "I want a pony!" is not a worthwhile critique of anything, it's merely a fallacy.

While I’ve added the critique to my reading list, I have yet to finish. I cannot speak to your claim the Illich’s critique is based on what he so desires (“I want a pony”), as opposed to describing a phenomenon of individual emptiness as a side-effect of Western institutions.

I agree if his long-form critique takes the structure you claim, it is of poor quality because claiming desires in not critical of anything.

However, I do disagree with your claim the critique alone is not helpful. A harsh, well formed critique is typically the very first pillar in driving change. Expecting identification and resolution in the same piece is asking too much.

I would argue to say that a critique being invalidated because it somehow must include both framing and describing a phenomenon as well as suggesting changes, each weighted by their feasibility in remedying the systemic woes, is much more fallacious.