I think most people would go back for their wallet unless either they were on a train and couldn't turn around, or they were already at their destination when they realized they'd forgotten it. The suicide option must be considered, but not much sleuthing about that can be done unless we heard more personal information from the family. I am no expert. But I don't think most suicides look like disappearances, as this does. There's a note, there's a body, there's something public. A father's suicide would be tremendously painful to his family, maybe he wanted to shelter them from that reality, and having no identification might help that as you suggest, but if he cared about them to that extent, why leave them in the dark about whatever he was struggling with? And, again perhaps I'm stereotyping, but based on his appearance and employment and life situation, suicide doesn't seem likely to me, unless he was already leading some secret life or struggling with hidden issues that he could no longer cope with. But a suicidal man, why would he go to a train station? I take the Long Island Rail Road myself and assure anyone unfamiliar that no one is ever hit by the train accidentally or suicidally without everyone knowing about it.
A train station is where you go when you want to go somewhere fast and relatively unidentified. A man leaving his family (if that's what's happened) doesn't take his car because it identifies him. Or his wallet, as mentioned. But a train ticket, you're anonymous. There's thousands of people riding that train every day and it's likely you'll go unnoticed. Once you're in the MTA system, you can get anywhere, Penn Station, the airport, anywhere.
It's really not our business, unless the family is asking for help, which they are. This must go without saying in these forums but the family needs to disclose a lot more information if they want the public's help, beyond just literally trampling through the woods. Were there financial issues? Were there drug issues? Anger issues? Depression? What happened that day at work? There has been no information about his work day, other than he was seen there as late as 12:30. Does he work in an office all day or does he go out on calls?
The wife said his car was found parked "in front row to the right of ticket booth..maybe 10 spots from end of lot." Looking on google maps, this strikes me as someone not planning on meeting someone in the lot, or being driven there against his will. The lot is very large. It seems, to park where the driver did, he wasn't looking to hide the car. He was likely looking to catch a train, maybe quickly. There is a very large conservation preserve adjacent to the station, called Edgewood. Some searches are being focused there. But where the car was parked, I don't see the connection. The car was parked relatively close to the ticket booth, not the preserve. You would have to traverse the whole parking lot from the car, and then cross over an avenue, to get into a main part of the preserve. The only way that the preserve plays into it is if the car was intentionally parked near the ticket booth as an intentional misdirection. What criminal masterminds out there would really do that though?
Or a suicidal man?
I'll add that I understand the searches and would never actively discourage them. People are looking for anything they can do, and you never know, sometimes the oddest improbable things can indeed happen.
There's a note about how the seat was pulled forward, not how it was normally. That's of interest. Maybe it is possible after all that he met with foul play and someone else drove the car and made a getaway on the train. But that wouldn't be a random act of violence. For it to happen in broad daylight as he made his way home, it just doesn't fly unless the perpetrator knows the missing man and something takes place in private.