MD,
The only part of the "why" question that matters to an attorney is the financial one.
For the family, I think the "why" is not only financial but also something called DISCOVERY. Discovery means their attorneys get to ask questions that have not been asked or answered, or have not been answered adequately or properly by the authorities, in depositions or, as they call them in New York, EBTs or examinations before trial. I don't know what they are called in Quebec. Discovery is also done via service of assorted written requests, which are done either informally, or formally as freedom of information act requests, or in litigation as "interrogatories" and "requests for production."
Based on what I have read, the family obviously thinks the Laval police department is staffed with so many fat, lazy, donut munching morons who have not done their jobs. In the litigation discovery process, you get to take depositions in which you get to ask those fat, lazy donut munching morons if they did what they were supposed to do in investigating this case. Will this lead to the discovery of any new information or leads? Maybe, maybe not. For me, that is the fun part - getting to ask the questions that should have been asked. That's what my clients pay me to do. For the family, they hope to hear answers they thought should have been coming earlier.
You will maybe learn the name of the taxi driver (you subpoena the taxi company's payroll and attendance records) and if he is ID'd get the name of the executor of his estate if he is dead. Your get to learn what was on the fence (subpoena the quarry's records to get the name of the fence company they used), whether there was illuminating in the area where they climbed the fence, if any (you will find this out when you get the name of the fence company and subpoena them). It's possible that you will identify witnesses who have not come forward and given statements to the police, for whatever reason. I suspect that the Red Lite personnel on duty that night could also receive subpoenas.
It should be noted that there were media reports that did not identify the taxi driver but said he committed suicide. Wouldn't you want to know who he was and why he killed himself if you were the family?
In summary, a lawsuit will allow the family to conduct their own investigation through what is called the DISCOVERY PROCESS.
I have handled a few wrongful death cases and in addition to getting compensated, your 5 step process leaves out something that is very important: getting information about the deaths of their loved ones that the authorities failed to obtain and/or is not giving out. That's why they need the discovery process. I am actually very surprised by your question, because this answer should be fairly obvious if you have read the many media reports on this case which Captain Renault has been kind enough to post. These families do not feel that the investigation identified what happened to their boys, so they will try to learn the truth through the discovery process in litigation.
Is it right for them to second guess? I don't have the answer for that and I am also biased, because I get paid to second guess everyone for a living. You have to answer that question by supposing that your sons or daughters were in the same situation and befell the same fate as Kraynak and Wright. Would you want those answers? Or would you want closure? I find that it varies depending on the client.
It was posted above that the coroner's office did not share its report with the family before releasing it publicly. Here, doing something like that is unthinkable. That kind of shit invites litigation. It is BULLSHIT as far as I am concerned. It seems to me that the Laval authorities did not do a very good job communicating with these families and now they be embroiled in litigation discovery because of it. You don't think those families want to see the coroner's report????????????
In the litigation I have been involved in, a very good percentage of it is started by miscommunication between the litigants that one or both feels must be resolved by the Courts. It is the way of obtaining closure for some.