I understand salted butter can be useful is some situations, but why there's no such thing as "sugar butter" that can be sold in stores? I mean, there is sweet milk (concentrated, for instance) and sweet yoghurt, but no sweet butter nor sweet cheese. Is it just cultural or is there some chemical explanation behind it?
Butter traditionally has salt in it as a preservative, mainly to stop bacterial growth on the residual whey, and to slow fat rancidity
Modern butter has a much lower amount of salt than is required for shelf storage in the pre-electric era. Now we have refrigerators, salt is not required at such a high level
Butter with no salt has nearly half of the shelf life of modern salted butter
Processed sugar is a modern ingredient, and therefore there is no culture in having it in butter.
Sweet yoghurt and milk are all "new" inventions
Using salt as a preservative is as old as recorded history. Many cultures used salt to preserve fruits, as well as meats and vegetables
There is such a thing, for example Corriher has a great recipe in Cookwise for chambord butter. These foods are of course not pure butter, just as "fruit yoghurt" is not pure yogurt: you can mix butter with sugar and sweet flavorings to make a sweet butter spread, like you can mix it with parsley and chives to make a savory spread.
As to why there is no commercially mixed sweet butter readily available, I suspect that this is a simple case of the law of supply and demand. And the missing demand for certain foods globally (like sweet butter) or locally (like cream of tartar) is an interesting sociology problem (I suspect it is due to the cooking styles in certain influential books like Better Homes and Gardens in the US and Dr Oetker Kochbuch in Germany), but it has no real culinary roots.
Bacteria loves sugar. Butter with sugar added will spoil in a few hours at room temperature unless preservatives are added.
Two reasons. Butter is sweet. Butter is a base ingredient. How would one determine the level of sweetness and what would it be used for. How would sweet butter increase sales over plain?