I actually just bought the 28-300L as a travel/walkaround lens. I'm not fussed about the weight or size - it's not significantly different than the 70-200/2.8 II or the 100-400, and I'm also comfortable with the push/pull zoom. My current 'walkaround' kit is the 24-105mm + 70-200 II, so the 28-300mm is lighter and means no lens changes - useful when I'm already juggling two kids.
The 24-105 + 70-300 L would have been another possibility, but still not lighter in total, and still requiring lens changes. Compared to that, the 28-300 isn't much slower through the range - for me, f/4 and slower generally means a flash indoors, and even f/5.6 is generally ok outside.
The only concern I have is IQ, but it looks good so far. It's a superzoom, so there's distortion - but in fact, the barreling at the wide end and pincushioning at the long end aren't even as bad as on the 24-105. Likewise, sharpness is pretty similar.
So...overall, I think the 28-300mm will make an excellent walkaround lens, for me. It helps that I also have fast lenses, if I need them.
@JTPAIN, I think not for you - I'll be using it on a 5DII where it's moderate wide angle to telephoto. On APS-C, you would lose the wide angle, making it much less useful, IMO.