Do you use 5D III plus 24-105 as travel camera?

My guess is you will shoot exclusively with the 5D3 once you've tried it. The 24-105 or the 24-70 II would be my advice for all-purpose lenses with the 24-70 II being noticeably sharper especially at the wider apetures.

All of my non-business travels center around photo/hiking trips to National Parks in the West and Southwest USA so, my whole kit (or 2/3s of it) goes with me (check my geat list). My cameras and the most essential lenses and filters get packed into a Lowepro Computrekker backpack, the next tier of lenses & the rest of the accessories get packed into the larger of my Lowepro Carry-on Certified roller cases, and the rest of my lenses, mostly Zeiss primes and a few of the Canon less-used lenses go into the smaller Lowepro Carry-on Certified roller case.

When I fly, I use the backpack and the larger case which I re-pack according to what I think I will need. I have been lucky enough to have been allowed to carry both of these onto AA flights so far, and when I travel by car, everything goes. These kinds of trips are why I buy this stuff so why leave anything at home if I can help it? Yeah, it's a little bit of a hassle toting the stuff during the actual travel part of the trips, but...the pain is brief.  Obviously, on hiking, I have to leave the vast majority of my equipment in the room or car but at least everything or nearly everything is with me and not 2000 miles away so that I am allowed choices.

On business trips, I am rarely interested in photography anyway, so I snap with my iphone if I snap at all.

Not sure why you would want to limit yourself to one lens. It's not what DSLR is all about. Are you opposed to wearing a lens-specific pack to carry extra lenses during walks/hikes or using lens-specific carry-on for the flights? My stock advice for newbies (which you do not appear to be one but it would also apply to anyone new to Canon) is to build your kit around the very best zooms in the range you normally shoot. For me, that would be UWA to 200mm. The lenses that fit that range would be the 16-35 II, 24-70 II & 70-200 IS (either the f2.8 of f4 - I have the f4 version) and at least these three should go with me wherever I go. If one is following this advice, primes can be interjected as needed and/or can be wedged into the budget.

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Rick Knepper, photographer, non-professional, shooting for pleasure, check my profile for gear list and philosophy.