Why should it?
I mean, it's a common conceit in science fiction that faster-than-light travel requires some sufficiently `flat' spacetime. That's a good way to explain why the characters need to have spaceports and space stations and the like. But it isn't like space near the surface of a planet is that curved. It's detectable, surely, but if the warp field equations are so sensitive that the difference between the flatness of space near the Earth's surface and the flatness of space in, er, space matters, then they're surely too sensitive to be used in practical applications.
In any case we've seen going to warp from sea level isn't apparently a problem.
Except we're not talking about warping space at FTL speeds, just generating a subspace field sufficiently enough to lower the inertial mass of the ship - much as O'Brien did in the pilot episode of DS9
I think this is my problem. I'm not a physicist so I get very confused trying to work out the physical parameters for Trek tech and when the writers move the goal posts I get even more confused. It seems to me that if you are warping space to go in a direction, you are warping space in front of you and it snaps back into normality behind you so your navigator needs to make sure that there is nothing significant in your path that might be crushed and/or slam into you and if you generate a space warp in an atmosphere then all the atmosphere in front of you is going to be affected by that warp. This would disrupt weather patterns (fine if you have weather control satellites I suppose) and might wrench a chunk of your atmosphere out into space because you are drawing a vacuum into that atmosphere. It just looks a bad idea to me.
If you are going to generate a warp field to reduce the pull of gravity on your ship by reducing its mass then I would have thought you need to warp space between you and the object that is exerting its gravitational pull i.e. the planet, so you are warping space behind you. So while I agree that in the grand scheme of things you would not require much in the way of a warp field to do that, complex life forms tend to be adapted to a very narrow band of existence and are very squishy when their conditions are altered. What happens to the life forms that exist between you and the gravity source when you warp the space that they're in to let your ship pull forward a bit easier?
The only thing I know that warps space at the moment is gravity but I think that conventional warp fields are based on purely gravity warps or travelling at warp really would play havoc in solar systems wouldn't it?
I rather like the tech having limitations and drawbacks so I suppose I don't like it when I see some new magical technology thrown on screen to look cool if it makes a mess of my understanding of fictional world physics. Reversing at warp actually seems a lot more straightforward to me, since you just need to extend the warp field in the opposite direction.