The speeds required for planes to fly are speeds relative to the air, not relative to the ground. You are correct that taking off with the wind will require less acceleration to get to a certain speed, but that speed is relative to the ground, so you might not be at the required air speed.
Picture a runway left to right. A plane on the right side wants to take off to the left, and a wind is blowing. Consider two cases:
- The wind is blowing left to right(headwind). Any rightward wind speed can be added to the plane's leftward ground speed. If the plane can take off at, say, 50 kts, if the wind is 10 kts, the plane's required ground speed is only 40 kts. The total airspeed is 50kts.
- The wind is blowing right to left(tailwind)
Any leftward wind speed must be subtracted from the plane's ground speed to get airspeed. Again, trying to reach an airspeed of 50kts, a tailwind of 10 kts will require a faster ground speed. The aircraft's speed relative to the ground will be 60kts before it can take off, though the instrument airspeed will only measure 50 kts.
So, for those cases, there is a difference of 20 kts ground speed. It can take a bit more runway to get to 50 kts airspeed if your ground speed is even faster than that. Most pilots don't enjoy running out of runway.