As you know, あります and です are not the same. However, です can be written as で あります. (Some say this is where the word です originally came from)
Similarly, ございます (humble equivalent of あります) and です are not the same, but です can be written as で ございます (again, if you intend to be formal and humble).
So, neither あります nor ございます can be replaced by です just like that. You could of course theoretically say はやいです (it's early) or ありがたいです (I'm grateful), but it would be odd to use these instead of the fixed expressions. In fact, they're called fixed expressions for a reason: there's not much point in trying to analyze them, let alone change them.