No, because you spend some of your forward speed flying into the wind to keep the desired ground track.
Imagine an airplane that flies 100mph. You want to fly north, but you have a 90pmh crosswind from the east. You have to point almost directly into the wind just to keep from getting blown off course. You can turn a little to the north, and you'll go very slowly. If you instead have the wind come from the east, you still have the same problem.
Maybe easier analogy: to get directly across a river, would you rather swim across one going fast or slow?
Sure, with a consistent cross wind of course you'll have to spend energy fighting it, but if you don't fight it and halfway it changes, you'll end up at your destination in the same time as you would have otherwise, no?
Sure; if you can predict the future, and the future happens to be that the crosswindws will oppose each other, then you can just set your heading and get there.
However, if the wind doesn't shift you are now taking even longer to get there because you'll have to turn to go straight upwind once your destination is directly upwind from you.
This crazy world you describe applies in a different axis! Vertical movement of air happens on a much smaller scale, so it tends to cancel out as you fly through it. If you climb in the updrafts and descend in the downdrafts, you only make it worse. Better to ride it out.
The US air traffic control system is setup as a series of highways in the sky. You generally can't just fly in whatever direction you want (with the exception of general aviation).
Imagine an airplane that flies 100mph. You want to fly north, but you have a 90pmh crosswind from the east. You have to point almost directly into the wind just to keep from getting blown off course. You can turn a little to the north, and you'll go very slowly. If you instead have the wind come from the east, you still have the same problem.
Maybe easier analogy: to get directly across a river, would you rather swim across one going fast or slow?