OP, I think this is a great question and needs to be asked more often.
my personal answer is no, because psychiatrists, forensic psychiatrists, and criminologists often link danger to self with danger to others under this common notion of safety. A criminologist would likely say a suicidal person is more likely to be dangerous to others. Because these are things considered to have covariance, they wouldn't really be able to measure one without implicitly looking at the other, so suicidality would still indirectly impact risk assessments under your concept and would be a possible back door to involuntary hospitalization.
but i've had horrific experiences with psychiatry and for ordinary people, it would possibly create more trust. it would be a less awful standard.
for many people who are involuntarily hospitalized, they bear the cost of the stay ($20K? 30K? 40K? 50K+) and the costs are huge, the hospitalization may be able to preclude the patient being fired due to the absence, but income does not automatically come in, nor do bills stop. it's not just the loss of autonomy. involuntary hospitalization is horrendously expensive and financially disastrous and often the amount of treatment relative to the high costs is a terrible value for patients and extremely lucrative for practitioners. really, this comes down to doctors not wanting to be blamed if something goes wrong, and so it's financially more lucrative and less risky for a doctor to recommend involuntary hospitalization, while rarely better for the patient, and it may be better or worse for society but it's hard to know.
We also don't really know with any certainty whether involuntary hospitalization causes suicides. It's so hard to isolate that variable but my guess is it does. (There's no way to perform the experiment because without liability since the study would be considered unethical: you'd have to take people who were all edge cases for involuntary hospitalization, right at the border, and hospitalize some and not hospitalize others using a coin toss or randomized method and then wait to see who dies; and to be a valid longitudinal study, there would have to be a lot of people in the sample. The mental health industry also makes tremendous amounts of money on the suffering of others and so would be incredibly disincentivized from finding out if involuntary hospitalization increases suicide rates; we will never know, no one will pay for the study and accept the potential liability of doing so, and a research organization or research professionals would be needed to perform such a large study properly so it's valid.)