I'm from Czech and pretty much everyone under 30 speaks fluent English. Old elementary school friends could hold a normal discussion without skipping a beat.
But boy, the second I went into the old part of my childhood town and wanted to get some food from the bakery, not a single person could understand English (which is fine because I speak fluent Czech).
I had a situation about a decade and a half ago when a french person stopped by a gas station and the clerk could not, for the life of him, communicate with the french guy but within ten minutes, a bunch of teenagers were able to translate.
So it's not just official stuff (which makes sense) but also an age and location thing like you said. If you break down on the high way, stop at an old town, or try to deal with an establishment is generally run by someone over the age of 40, you can find yourself in an uncomfortable situation.
In bank or medical situations you can run into situations where even though the people all know English, they might not have the necessary vocabulary to express themselves in English or lack certification proving they do. Anyone who doesn't want to fuck up simply won't use English and require a translator.
I think this is something different in Denmark mainly because, since it's such a small country, a Danish person in these sectors needs to be comfortable with the relevant technical English vocabulary anyway, even when not interacting with foreigners. Many materials are not translated into Danish, especially when you get past the introductory textbook level, so there's an expectation that if you're in a high-skill, university-qualified profession, you can read/write and speak professional English. ("Professional" here meaning that you have a working English knowledge of your own profession, not necessarily that you can talk about all subjects in English.)
But boy, the second I went into the old part of my childhood town and wanted to get some food from the bakery, not a single person could understand English (which is fine because I speak fluent Czech).
I had a situation about a decade and a half ago when a french person stopped by a gas station and the clerk could not, for the life of him, communicate with the french guy but within ten minutes, a bunch of teenagers were able to translate.
So it's not just official stuff (which makes sense) but also an age and location thing like you said. If you break down on the high way, stop at an old town, or try to deal with an establishment is generally run by someone over the age of 40, you can find yourself in an uncomfortable situation.
However, I'm kind of surprised at the bank thing.