I think it's because the term "commit suicide" implies a moral judgement, in the past Western notions of suicide were actually pretty barbaric. To accuse someone of trying to commit suicide would have been a fairly serious accusation, in fact in the past in some jurisdictions suicide could mean that your estate went to the government instead of your family as suicide was seen as an offence against God and the Crown.

Nowadays we tend to recognise it for the complicated set of behaviours that it actually is, modern notions of mental health and other factors that can contribute to suicide are often no longer seen as personal (and sinful) moral failures on the part of the suicidal person. To "commit" something usually implies that wrongdoing has taken place, for example as a thief or arsonist commits theft or arson. Since suicide is often the result of severe mental health issues, intolerable trauma, or other factors that have nothing to do with a person's moral conduct the verb "commit" is often seen as inappropriate in modern discussion.