That probably depends on the country, but I don’t think you should omit learning language, even as English native, even if everyone around you speak your native one.

I've seen that several times already in Poland. Been around a guy from India who was practically monolingual English speaker (his local language is fading away, he should technically still speak it due to his grandparents, but doesn’t or speaks very little) and he straight up refused to learn Polish because he „seen no value” in it, it’s not an easy language to learn and he'd rather just put that time and effort into a MMO game. He only attended lessons to learn to pass an exam that will allow him staying in the country, with no intention to actually learn how to speak. Poles are quite often excited to speak English with somebody as everyone knows importance of it and wants to practice IRL. Everyone around him, like his gf, her family, coworkers in corpo, accept that and they all speak English well, so no obligation on his side. He only knows how to tell cashier that he'll pay with a debit card and it takes a single word. Well, that’s his choice you can say, but then it was pretty annoying at times to have him around. Imagine standing in a circle joking around and every two sentences that guy asks „What? What did he/she say?”, and someone attempts to translate it to English, but the joke doesn’t work or is not understandable even after translating because it refers to something else in the language, culture, memes, slang etc. Either learn it or expect to be disconnected and excluded at times. That’s all good to tolerate newcomers who don’t yet know much about the culture and language, but it doesn’t look very good to me if that’s a guy who lives here for 8 years and doesn’t have plans moving away anytime soon.

The EU isn’t the US.

Most countries in Europe have this idea of integration where the foreigner learns and adopts the language and culture of the country. You’ll see lots of discussions of “failed” integration of foreigners, especially in Germany.

I think this is still a type of colonialism where they think there culture is better and the foreigner must change, rather than the other way around.

I think the US is a bit better in this regard as there is this idea of a cultural mixing pot and foreigners aren’t expected to “integrate”.

It's not just communicating, it's also stuff for general living, like recognizing road signs, paying bills, dealing with government paperwork, ordering food in restaurants, etc. They won't always have an English translation beside it, nor do they have an obligation to have it. Same goes for people too.

Say for example, a Japanese just showed up in your hometown, knowing not a lick of English, and planning to live here long term. I'm sure people in your hometown are more than willing to help, but how much stuff in your general life is in English? Surely you can't expect someone to be able to help them around 24/7, and with a language barrier too.

You gotta know that not everything is going to accommodate for you in foreign places. OP might be able to do well enough since people in Denmark probably speak English well in general. But if you want to truly know the people, their culture, or even form deep connections with some, you have to do some work, and language is a first big step.

This is the absolute worst advice for coming to a European country. It's probably different in Denmark but for some countries or cities at least you won't be able to get through the bureaucracy needed to legally immigrate without speaking the language. Even in offices that mainly help foreigners you may find the employees don't speak English. And if you want to be there long-term, good luck making real connections if you don't speak the language.