None of the ships are designed for it and unless we completely neglect any notion of realism, all of them would crash immediately. You need actual wings with engines to fly within an atmosphere.
You could make the same argument against atmospheric flight for No Man's Sky, but it's going to pull it off just fine. There's no need for atmospheric flight to feel the same in Elite as flying a plane does in real life and plane sims at the moment. These ships have shields, remember? The shields protect against physical interaction with its surroudnings. In effect, the ships shield should make it slip through the atmosphere as if it were still flying in space. There would be no buffeting by the wind or any kind of turbulence experienced.
What I think the real issue will be is adding enough realism to planets to make them feel worthy of exploration. No Man's Sky always intended to do space and planets at launch, so they built their engine from the ground up to support this. NMS' procedural generation is very sophisticated, more so than ED's (as far as I can tell) at the moment, but that's okay because NMS isn't shooting for a super realistic look; ED on the other hand
is. So they needed to delay such content for a later date. Bear in mind, the original Elite had planetary exploration, although primative it was still extraordinary for that era of basic computer games. No one expected anything too special from the planet surface's because computer graphics of that era couldn't do anything too detailed no matter what kind of game it was, so for the punters of that era, it was just fantastic to be able to enter the atmosphere of a planet and look at a big green landscape with a few triangles representing trees and then a line of blue or a field of blue to represent rivers and oceans respectively.
I think what FD will be able to learn from NMS and upgrade their procedural generation engine to make detailed worlds with caves and mountains and forests, deserts and icy tundras with animals as well. Barren asteroids and moons are a good place to start, because they can develop the bones of this procedural engine to make basic caves and rocky mountains and valleys without having to worry about complex flora and fauna. Once they've got those bones working right, they can build on them to include said flora and fauna.
I know where you're coming from,
Magnetic Sun, but FD know that Elite Dangerous has many fans of the original Elite and these people expect a modern iteration of that game. You need to be able to do everything you could in that game and more, and that includes planetary flight, and by extention
explore these planets, as exploration is what's expected from a modern version of Elite. This is even more important with No Man's Sky looming on the horizon.