I see that point (well, those 10 days will pass regardless of where you are...so considering really just the 1,000 mile journey)
And if those 10 days pass while I am at home, I have rifles there.
but the statistics folks also say that most accidents and general trouble happen within a few miles of your home.
Because you spend the majority of your time at or within a few miles of your home, I think.
Ok, but yes, that is mighty specific. You're envisioning one kind of trip where you work around the rifle, and can without too much trouble because you aren't doing any of the things that most folks do when traveling.
(Staying in hotels, etc., etc.) Your specifically chosen trip is almost tailor-made for accommodating having that long gun around. In order for 95% of other travelers to be in the same position, they'd have to radically alter/curtail their normal travel accommodations and itineraries to make happen the conveniences you're taking for granted.
It's a bit like the "well I might happen along a spot to stop and shoot" suggestion. If you've stacked the deck very heavily in favor of that (e.g.: locating shooting ranges along your route, traveling through BLM land --or-- staying only with relatives and not entering buildings out of sight of your car along the way) then it starts to be more reasonable.
As a simple matter of course for a gun owner on a normal trip, it would be quite the opposite: A hassle and bother to deal with, forcing extra care and adjustment of travel arrangements the only rationale for which would be the galactically, vanishingly, rare occurrence of a self-defense confrontation in which a rifle was accessible AND the only sufficient tool.
I guess I'm just fortunate, for now, in how easy it is to bring a long gun along.
Although much of my somewhat-recent travel didn't fit that description exactly either, and I still brought a long gun...but it was just a Remington 870, not an accessorized AR, and I was certainly happy to have it in our rented domicile for the week considering the local bear presence. (Rockies, Tetons, Rockies again)
Didn't bring a shotgun to Alaska though. Had too many checked bags already. Settled for a .44mag to supplement the .45 on that trip.