Yes it is great when support is shown after the fact. But what about before the suicide?
Too many do put alot of faith in CISD. Some will go through these meetings doing and saying "what is expected" and not really expressing how they are dealing with the problem. If it is a macho department and people are joking about having a 6 -pack of beer, then much is lost in what CISD was intended to be.
Few are going to talk about their personal problems that deal with deep emotions or financial problems, sexual issues, identity issues or drug and alcohol problems. EMS, the FD and LE are all known for looking the other way when alcohol could be an issue. "He can handle it" is too often the mentality meaning that you look the other way. "As long as he doesn't drink at work" is another which for some you'll never really know how much they are drinking at work. Knowing someone is doing illegal or legal drugs but to excess is another problem when some don't want to "rat" out their partner. Knowing someone is drowning in financial problems but don't want to embarrass the person about getting some help can be a biggie that unfortunately leads to suicide. Marital problems that aren't just the normal squabbles but ones that affect a person's mood drastically is another sign their life might spiral out of control.
So yes, EMS, FDs and LE are great after the fact but many will say "never saw it coming" but in reality they may have brushed it off or looked the other way.
Having a nice funeral isn't the way to really help the person who committed suicide although it is a nice gesture to the family.