The issue for me has not been one of wanting the parachute with me for safety reasons (what circumstance would require bailing out of a 727 that wouldn't best be served dealing with it in another manner? Yes, the unfortunately obvious scenario comes to mind, but the odds, despite everything, are incredibly low). For me, the primary reason I travel with my rig with me instead of checking it is a simple matter of cost. I have about 5 grand in it. I really don't want to depend on some idiot (i.e. someone not me) to get it to my destination. I've had too many instances of my luggage arriving days after I do, and at least one where, by the time the airline found my luggage, I told them to just send it back to ORL and I'd pick it up there the next day when I returned from my trip (2 week stay in NYC). If I'm travelling with my parachute, it's because I want to use it, not so it can fly all over the US while I wait at my destination.
I've never had delays going through security with my rig. I always check to make sure the AAD is off when I leave home and I pack my hook knife in my checked baggage. While I have had a few quick trips in the past to Rome, Ga where I didn't want to pack a carry-on, I simply left the hook knife at home and kept one at my friends' house to use while jumping there. Normally, security just flips open the covers for my main and reserve and run their chem tests and that's the end of it. I also typically do NOT follow the USPA recommendation and pack my rig in a bag. The bag takes up more space, and I often use as my checked bag and put my clothes in it along with my miscellaneous equipment (the aforementioned hook knife and helmet, altimeter, jumpsuit, etc). However, on light trips, I have put a change of clothing and my gear in the gear bag with the chute. I simply pack it all one one side of the container to make it easier for the TSA to take the rig out if they want to.