Trump is and always was a Builder first. Being that, you deal with many shadey characters, "even the bosses", let alone Union Goons, and Wise guys, "gangsters".
They are heavily involved in the Cement Steel, Union, and labor Racketeering. Remember Hoffa?, It would make sense that when he was starting out, the thought occured that he may sometimes be in a position where he could need a gun, aside from the obvious idea that when you carry money and expensive Jewelry and cars, you are a target in just about every big city.
If I had to guess, having lived a few minutes from where he did, in Queens, and also having a Permit, "carry", that having it for such a long time, one becomes used to a gun being there. The idea of not carrying one after 20+ years of daily routine, can make you extremely uncomfortable. Especially if that gun saved your butt once or twice. I would imagine, that he would like the option of being able to carry, even if he didn't most times.
Like having one in the Bedroom like Reagan said, "just in case". We all know strange things happen, so why not opt to continue what worked before Pres or not.