I'm pretty sure that's just how they are. My P10F has the same loose fit, but there isn't a way for the pin to walk out enough to cause a malfunction because of the way it sits in the frame. In fact, I can push the pin into the assembly with my finger, no punch/hammer needed.
Try the new pin, but I bet it isn't going to be tighter since it's the hole in the trigger and the trigger bar that retain the pin and make the tight fit, and I doubt you've been taking the pin out over and over based on how little marring there is to the pin finish. If anything is worn, it'll be the trigger bar hole (which is oversized already if I remember correctly to allow the trigger to rotate) or the polymer of the trigger shoe. The polymer isn't likely to have worn the steel pin, so I bet it's the trigger shoe hole that's just a hair too loose.
I would just push the pin back into the center of the assembly and live with it.
Loctite it if it bothers you, but there really isn't any way for it to put you in danger as the pin can't just fall out or protrude enough to entirely block the trigger. It might actually make the trigger pull heavier depending on which part you loctite and the tolerances involved. Remember, that pin is a pivot point, so at least one set of surfaces is a bearing/bushing.