Of course it works like this. We have transformed into a society where risk elimination is critical to one's career. It goes much, much deeper than this.
What you neglect to mention, for example, is that therapists will do the same. As soon as they believe a suicide wish is realistic, they will do anything, including declaring the patient entirely healthy, to get them out. "Refer them" (ie. "go somewhere else"), declare them healthy, fall ill themselves, whatever. The alternative is that sooner or later they fail with a kid, which ends careers.
This means in practice there is no help with suicide. Not for kids, and not for adults either. If you have a real problem you will not be helped. But that's not the end of it. What will happen if you DON'T have a real problem? These institutions ... are paid per-patient.
So social services WILL lock up kids who express anything about suicide. "For their protection". On the aforementioned condition that they are very sure the suicide wish is NOT serious. These institutions get into the news regularly for the serious child abuse that happens there, and are legendary for how badly they take care of kids. No serious education (no more math, "rap lessons"). No going out. No TV. No contact with friends (oh! the risk!). They take away any prospects at a future, any reason to want to live.
That's where the money is in therapy: "treating" very, very light problems. Problems so light they wouldn't exist without therapy. And, because kids usually don't want this, forcibly treat them. Hence the "need" for closed institutions. Not so much to keep kids away from ways to kill themselves, but because they'd never see a therapist even once if they weren't locked up. And no patients ... no money.
Research into the subject regularly comes up with the observation that ... suicide does happen at such places. In fact, much more than in "free" society. Which seems strange, since they refuse any serious patient. You know, if a hospital were to only admit patients that do NOT have cancer, it's very weird to observe cancer deaths at such a hospital. But that's exactly what happens here. There is much discussion, which mostly focuses on that diagnosis (which such institutions don't do and therefore go blameless for) doesn't work. That they regularly get much more serious cases than they bargain for (thereby usually admitting that they use psychological diagnosis to AVOID helping real cases, but THAT problem doesn't need solving. The problem that needs solving is that psychological theory doesn't allow them to be effective enough at avoiding real patients).
But there's another, very obvious, explanation ... that these places, these treatments, rather than treat suicidal ideation, in fact cause close to 10% of kids admitted to commit suicide, when if you'd literally told those same kids that no help was available, at most 3% would have died through suicide. And that's assuming they do actually take serious cases, which they don't.
Things make a lot of sense if you realize the obvious: that help, social services, and child "protection" is built around the need for them to make money, either directly or through subsidies. And then they proceeded to hire a bunch of MBAs to maximize this money (so "known effective" methods, such as hiring highly educated well-paid individuals to take care of such kids) never happens anymore.