1. The plane has to fly sufficiently fast (to avoid stall), and sufficiently slow (to avoid "Mach tug"). As one flies higher (air density sinks), these two speeds converge, forming the dangerous "coffin corner". Now, in general, planes don't fly as high as possible, I'd say, so that there is some leeway in terms of chosen airspeed.

2. For given airspeed, the plane flies less time with a tailwind than a headwind.

So, this does save fuel, I'd think.