I can't think of any specific thing preventing this in general. An atmosphere is basically just space with some density (Earth's atmosphere extends far into areas often depicted as stable orbits in Star Trek).
It's basically the same compared to jumping from within a nebula or similar phenomenon, which is something depicted rather often in later series due to advanced CGI capabilities.
However, there could be specific influences, like gravity or density making it highly unattractive, e.g. due to additional stress for the deflectors. As such it might not be standard practice.
But why do ships regularly leave it orbit first? It's most likely for easier alignment. Remember that even smaller planets will apply gravitational pull to anything nearby. Even when traveling to the Moon only, half a degree can make a massive discrepancy. The lower outside influences (gravity, aerial drag) the easier it is to jump into the right direction.
Last but not least there's something often ignored in Star Trek but depicted in the remake of Battlestar Galactica: The ship's warp bubble will most likely "pull" everything with it that's inside it - not just the ship. As such you'd basically cause a giant implosion the moment the ship disappears, even if you assume only the ship itself is moved (you can ignore the different drive technologies; the issue is the same):