Yes it is no doubt useful to learn the primary language of the country or area you live in. It's something that comes up often in my home country, which is bilingual. Most immigrants (refugees or otherwise) choose to learn English over the other official language, French. In Quebec, where French is the first language, but English is sufficient for some jobs (although not a ton, since many require French) and generally sufficient to get around town and buy groceries and stuff. I am bilingual and when I lived in a bilingual city I did my best to speak to people in their desired languages rather than relying on English, which is my native tongue.
I moved from Canada to the US, in an area where English is the official language but Spanish is spoken about as often as English. No hablo español muy bien. I've been working on it, I do audio lessons every day. I take it seriously, I think it's an important part of living here. I would say that English is certainly more useful, but it is totally possible to be gainfully employed while speaking Spanish. In fact, in some areas Korean, Chinese, or other languages might be enough to get through the day. But government services are a mix of English-only and English+Spanish so there's an obvious reason to learn at least one, if not both, and probably English before Spanish.
I was drawing from that experience to ask here. Non-German Europeans are permitted to reside in Germany. They do not enter as refugees, of course, and in general we would expect that most of them are more educated. Moreover, we would expect that most who live there long-term would learn German as part of their integration process. But we would not expect to expel them if they failed to, particularly if they were able to stay employed speaking a non-German language.
For example, I am also a UK citizen. As such, I can live and work anywhere within the EEA, including Germany, as can all other UK citizens. Most of them do not speak German. And of course we recognize that learning German would help their ability to succeed in Germany, no doubt about that. But they could theoretically go get access to some jobs without German, particularly if they were educated. As a matter of public policy wisdom, would it be wise to eject Britons from Germany provided they do not learn German, even if they are gainfully employed.
The idea of promoting German as a useful employment skill, offering German classes, requiring conversational German for further citizenship, tying German classes to unemployment aid or social services, etc. all seem useful to me. What I think makes less sense is making German compulsory just for the sake of the language, especially if that standard is not applied to other non-citizen residents.
Would you apply that standard to those who come from other EU countries but do not speak fluent German?
It strikes me that this broader issue is not about speaking German. All EEA countries readily accept other Europeans to live and work there without any test for fluency. I promise I won't take it as an insult if you tell me I should not be allowed to live or work in Germany, but I am, and I'm not sure how we can square this with the expectation here.
It strikes me that this is more about the cultural foreignness and "incompatibility" of those coming. Unfortunately trying to draw a line based on "compatibility" based on religion, country of origin, cultural values etc. is unpalatable, and so people find proxies, like language fluency, because those seem more rational and less discriminatory of a signal about willingness to integrate.
Like I said, it's very understandable to me that we would connect language to employment services, encourage it, make it easy to learn the language, teach the language in school for children, generally pipeline people into learning the language. I just don't see it as a sensible bright line because of how things are already set up.
(I also understand that the volume of new migrants poses a challenge that individual, voluntarily migration from other EU countries does not, but we generally establish rules and regulations that apply to individuals equally irrespective of their broader group membership.)
Now i am not integrated as well. I can't stand bavaria and the Oktoberfest. I am more the Pommes Schranke and Moin Moin german 
