What THE FUCK is it with the expectation that everybody has to understand and speak in-glitch? Employ a local guide. Too expensive? Bad luck. Entitled little .....
Not sure how random my selection process was, but that certainly wasn't my experience when I lived in Germany a few years ago. Maybe in big cities, yes. But even in the burbs, chances are you have to look for the metaphorical needle in the haystack to find someone speaking English. Your best bet might just be teenagers and young adults.
What does high mean in this context? I experienced what I would call the inverse Danish maneuver, the German obviously understand English because they often answered our English questions correctly - In German.
In Denmark if a Dane understands what you said in Danish but you have a definite accent they will often answer your question in English.
Maybe Germanic cultures are geared towards the rude.
If I'm talking to an Italian and trying to explain to them in English and they don't understand then I try with a combination of my broken Italian and hand signals, not obdurate sticking to English because that's being a jerk.
At the same time, yes Danes have a high English literacy, but switching to English when someone is talking to you in Danish is rude no matter how you slice it.