You can take a positional approach as black, but it is still a Kings Gambit. Even if white does not have an immediate attack, by the nature of opening the f-file, it is usually a wide open game and both sides can have king security issues. If you want to avoid the KG and other sharp openings, do not play 1...e5.
At the top level, the Ruy Lopez and Italian Game are considered better. Usually, when it is played at that level, white is playing for a win against a weaker player or due to tournament or match situation. There is no way to equalize easily. By contrast, with the Danish gambit, you can play early moves that do equalize and lead to little attack, so that is not playable above about the 1800 level. The converse of it being not used much at the grandmaster level because it is a little inferior, is that below the expert level, there is no reason to prefer the Ruy Lopez or whatever, because being slightly better theoretically is not important if both sides will probably make major mistakes.
There is also modern defense against KG and Bonsch-Osmolovsky Variation wich is very interesting.