It's not simply because the colour looks cool. Or because the characters hate pastels.
On the Final Fantasy XV forums, the game's director Hajime Tabata answered a question as to why all four characters were in black. Here's Tabata's explanation:
The clothing worn by the four main characters is the official battle gear of the Kingdom of Lucis.
Noctis is a member of the royal family and the other three characters are parts of various Lucian national organisations and they are each wearing the specific battle dress relevant to their individual stations.
In the Kingdom of Lucis where our heroes reside, the colour black has historically been treated as a special colour. Because of this, the attire of the royal family and those in occupations closely tied to them are unified by having black as a base colouring. This part of the lore is the reason why the outfits of all four main characters are black. For the finished game we also intend on having their clothing having effects in battle and not just being a part of the world and its background.
And here I was, thinking these dudes were the biggest Johnny Cash fans in the Kingdom of Lucis!