Crises over food and water would be bad, but a war fought over such crises would be an order of magnitude worse. I think if things were on the way to totally collapsing, you would see the war well before things actually hit bottom. I mean, by definition any such Giant Space War would have to be fought before the collapse was complete.
Climate, food supply, demographic issues are mostly growing worse, though the problem is very very manageable for now and the decline is incredibly incremental (it may even be reversible, if we get our shit together).
There's also a possibility that internal unrest in large powers will precipitate nasty things (I could also go about a possible friction-inducing social shift akin to the original introduction of Communism/Fascism, or the Reformation/Counter-Reformation, but I think it's kind of bullshit for me to argue about imaginary potential social shifts with no evidence for it at all).
Never underestimate people's ability to forget war's real impact after a long peace - or the capacity for stupid little bullshit things to spiral way out of everyone's control until events overtake everyone.
Anyway, I'm not disputing the points about globalization etc. The above stuff is just me throwing points out (those paragraphs don't even flow into each other very well). I agree that general wars area lot less attractive for a major power than they've ever been; "Greed will save the world" and all that. I'm just saying that a) it's not impossible and b) "not impossible" does not mean "a 0.0000000000000000000000000000001% chance".
The species has had a globe-spanning war about once every 75-125 years for as long as such conflicts have been possible (about 350 years, though some would argue for 450), and we've been beating each over the head with rocks for millennia before that. Wouldn't be the first bad habit we'd found was hard to break.
Maybe we really have turned a corner. Maybe our own mortality has sobered us up (a little). But I don't think we can say that for sure until quite a bit more time has passed.