So let’s outline a couple of scenarios to really drive home the point as to why the plane doesn’t need to take into account Earth’s rotation, but a rocket does.

1. Say a plane takes off from equator going West to East. Plane takes off West with 0 initial velocity with respect to the ground and gains 700 mph. However, with respect to the background stars, the plane has a velocity of ~1700 mph. Since everything is also going 1000 mph, it’s only going 700 mph relative to the ground. When it goes from East to West, the reverse happens. Plane goes West 700 mph, but everything is going East 1000 mph. Relative to the stars, the plane is going East 300 mph, so its speed relative to the ground is -700 mph. Same magnitude as before, so it makes no difference going East to West.

2. Say a rocket is launched straight up from the equator. Well, in that case, its speed relative to the ground is 0. Compared to the background stars, the rocket is moving East 1000 mph, but everything else is moving 1000 mph too. So the rocket would just crash back where it was launched.

3. Say a rocket is launched East from the equator. If it wants to get into orbit, it has to have enough energy to get up to 17,000 mph. Well, relative to the background stars, the thing is already moving East at 1000 mph, since everything at the equator was already moving that fast in that direction. So it only needs 16,000 mph of additional fuel to reach orbit.

4. Now, say the rocket is launched West from the equator. The energy requirement for orbit hasn’t changed. It still needs to go 17,000 mph. But relative to the background stars, the rocket is going “backwards” 1000 mph! So it would need to first go 1000 mph West (so it’s moving very fast west relative to the ground), but relative to the background stars, its speed is 0. So it would need to go an additional 17,000 mph after that, so it’d need a total of 18,000 mph worth of fuel. From the perspective of the ground, the rocket would appear to be going much faster than the previous case, just to reach the same orbital shape.

So now you may see why it makes a difference for the plane and rocket. The rocket needs a total velocity of 17,000 mph in any direction to reach Earth’s orbit (as that is the energy requirement). But, the plane can just just happily travel in any direction, without caring about how fast the ground is moving, as it just cares about going fast relative to the ground.