Just as the title asks, why does Super Sonico always wear those headphones? Is there a reason behind it, or is this just the design Nitroplus came up with?
I discovered an interesting piece of information to add to Dimitri mx's answer while I was researching my answer to Why is Super Sonico famous?. It turns out that Super Sonico was originally designed as the mascot for Nitroplus's music festival, Nitro Super Sonico, as documented on Super Sonico Wiki and Wikipedia. Nitroplus, though primarily a visual novel company, had apparently held this music festival for several years before they introduced Super Sonico as its mascot in 2006. In-universe, Super Sonico is a singer (and gravure model, of course); she had some very out-of-universe albums and singles released, which may have set off the tidal rush of Super Sonico love that resulted in the manga, visual novel, and anime.
So it made sense, when Super Sonico was first designed, to give her a pair of headphones: she was the mascot for a music festival, after all, and a singer herself. Dimitri mx's answer explains why she almost never takes them off.
Never Bareheaded: A character always appears wearing a headdress of some kind, and never, ever takes it off. It doesn't have to be a hat, any kind of headgear is fine. Furthermore, it doesn't always have to be the same headgear, the point is that this character is never seen bare-headed. This gives him a certain mystique, since while it might just be that he wears the hat because he feels like it, the fact remains that we never learn what his hatless head looks like.
Nice Hat: To show that you mean business, it's important to have style. Enter: the nice hat. It may actually have utility — even conveying special powers — but more often than not it just looks cool, or even just sexy.
Considering that Super Sonic is pretty much a half-naked model for Nitroplus, the Nice Hat trope "sexy" part does most certainly fit this description.
Character design distinction. Remove the headphones and she'll be any anime character with pink long hair and yeah, large oppai.
Conceal ears. Idk, I haven't probably seen an ear of a long haired female character.
Her headphones can be also sold as a character product so yeah, more $$$.
This is just my opinion though.
Sonico is a robot, pretty much. If you take the headphones off, she breaks. See this link:
In the game Sonicomi, there is a secret ending (ending 18), where if you touch Sonico's headphones she will say "- the demonic signal will be released and something terrible will happen! Everyone will die! So you can't touch them!". Touching them will result in a zombie apocalypse (https://www.youtube.com/watch?v=ROcp5DJQBu4). Not sure if this answers the question though.
She could be deaf and those headphones serve to help her hear, I mean if it is never addressed then it should be assumed that the information is common knowledge in that universe, maybe they serve to let her hear
I see them in a similar way as a blind man's shades, only with the augmenting ability that they let her hear