You are absolutely right.
It's a tough situation to be in and as human beings with emotions, we most likely will feel some sort of negative emotion such as sadness, maybe anger, anxiety, and panic. However, these days, the majority don't share their personal information online and you most likely aren't gonna have their parent's phone number to call, their school to contact, or even their hometown. We know nothing about these people, and that puts a block in the road when it comes to trying to help. I know it's hard to see someone go. The best thing to do is to stay level headed. Don't pile on. This may be personal opinion, but if you don't know the user very well, it's best to stay out of the situation. Leave it to the users they know and trust. Even they can't do much. Let those people be the one to talk them through the situation.
On top of that, most people aren't going to immediately become suicidal because of a single comment or argument online. Most likely, they already had those thoughts and tendencies. People argue, it's common. I think it's best not to blame someone unless they explicitly told or encouraged the other user to commit. In that case, that is when you report their account and contact moderation teams. Probably shouldn't attack those types of people either. It can create more drama, and possibly more casualties.
Maybe we should also reconsider our behavior toward others, both online and irl. It really can make a difference.