All you need is for orbits to intersect with the surface, not for a zero velocity vector at the surface. That is far cheaper to do than getting to orbit in the first place.
This absolutely applies to orbital mechanics.
Atmospheric braking makes it less likely to punch a hole in a skyscraper in manhattan when de-orbiting. And defacto raises ‘the surface’ in some senses.
It doesn’t change that it’s far ‘cheaper’ to go down a gravity well than go out of one.
Though that atmospheres (and liquid oceans) exist at all does prove exactly the point that I am talking about. The Sun and planets too, come to think of it.
If it was cheaper to ‘get out’ than ‘fall in’, none of those could exist.
Edit: I used a Hohmann transfer orbit calculator, and from an orbit of ~200km above sea level to an orbit intersecting ground level (0km), it only takes 203 m/s.
Without an atmosphere, it would be quite a show of course. But in this situation, that’s the point isn’t it?