Combat Air Patrols can guard large piece of sky, together with AWACS, they can still ensure air dominance up until a certain range from enemy installations, then you can safely use tankers behind them. Moscow or Beijng aren't that far from friendly, well defended airspace. 2 hrs of fuel will take you a long way, and then they won't be running empty, there's a lot of reserve. Forward operating bases will be more important in such conflicts for close air support as well as carriers, because you can't have jets on station all the time. You won't have fighter bombers in the skies all the time like in Iraq/Afghanistan, the fighterbomber will fly in and out. But before it goes in and on return leg, once in safe airspace, they still need the tanker. Taking off with a full load takes a lot of fuel, so once up they need to refuel to extend their range to the target and be able to make it back, even if they have to burn up a lot fuel to do evasive actions.
Unless you want to call everything peace time weapons, except ICBMs and nuclear submarines then no, they are not peace time capabilities and would still serve a major role in bigger wars. If Hitler had tankers, he would have bombed the US. And also the carriers, they don't have to be close to the coast and are well defended. USN also uses the Super Hornet as tanker, which can accompany the strike package up until a certain point and return when it has refuelled them. Su-24 and Tornado (Luftwaffe) also do buddy refueling.
Also, they would be needed to extend the range of the strategic bombers across the globe, so it can fly from Russia to close enough to the US, or from US to China. So those real 'wartime weapons' could still use tankers.
And your picture shows another point, when you have deployed forces, you need to keep the logistics line in shape, ships are slow. Strategic transports need to be refuelled as well to extend their range.