Fair enough, so in your opinion is war really a believable option? Can't see how anybody would profit from a WW3 really, especially how well connected the world is these days.
No. And it hasn't been since Churchills Operation Unthinkable in 1945.
We haven't had a war outside of secondary or tertiary territory since the end of WW2.
THere are several reasons for that, some underlying, some more at the surface.
First of all, lets look at war as an concept and in history.
In theory, all wars between countries can divided into two categories: Some broke out because one side thought they had something to gain, other because one side thought they had nothing to lose (anymore). Ignore religion, even those belong to one of either category.
As you correctly said, the world is so connected these days, that category two is pretty much out of the equasion. At least for developed countries.
So, category one then. What's there to gain in a war? Historically territory, resources and manpower. The last one is pretty much obsolote these days, territory as such even more so. Resources? Well, that's something else. We have seen wars for resources in secondary or tertiary territory (outside the developed countries/in africa), some even with some kind of involvment of our superpowers. So, why has there been no outright war in primary territory since WW2?
The answer is simple. The answer is MAD - Mutual Assured Destruction. For the developed countries, the assurance that an outright war always implies the possibility of complete destruction (even if winning the conventional war) has always outweighed any possible gains. It's a risk not worth taking and the reason the cold war is called the "cold" war.
We have seen, of course, deputy wars. Vietnam in the 70's, Syria today. Belligerents thought (or are thinking) there is something to gain over their opponents there. In Vietnam, it was at first the US trying to secure influence in south east asia, after the soviets gained influence. The soviets then intervened because they thought they could gain supremacy in the region, the US stayed because they wanted to counter that. After all, it was a pointless war. The USSR never gained what was sought, the US could've just ignored Vietnam because it was never as influental as some made it out to be. But well.
So, so much for the theory.
But today, why isn't it an option, even something like Vietnam?
Because Russia is still and will remain weak. MAD still functions because they kept their nuclear weapons, but both in hard and soft powers, Russia is no match for a United Europe even. A strong translatlantic partnership is Putins nightmare (that's why they want Trump...). So, for now, Russia doesn't have the power to actually challenge anyone, which also means there is no need for the US to counter anything. Crimea was significant because it was the first "war" for territory in Europe since 1945, but it also was a marvelous blck flag operation for a region nobody really cared about. But Putin knows he can't pull that trick again. So he's down to things like Syria and the concept of divide et impera (Trump! And of course, his financing of various right wing parties in Europe) to relatively upping his soft and hard powers by undermining those of others. That's his game, not actual war.