In grammar it's the WORDS which are singular or plural not the things they describe. The same goes for masculine, feminine and neuter words found in most Indo-European languages . Die Regierung ( the government) in German is feminine but it's composed of both men and women . The WORD is a feminine singular and is treated as such . The English word government , a body composed of men and women.It has no gender but is also singular , the plural being governments.
Die Regierung ist eine höchsten Institutionen eines States . The government is one of the most important institutions of state. Nobody in Germany would dream of saying " Die Regierung sein eine "........The government are one of .... The same goes for French , Italian, Spanish and the other members of the language group of which English is a member. These peoples have not allowed semi- educated people to step in and savage their language the way English language ( or is that now the England language ?) has been savaged.

I maintain that England is (are) a country and not a euphemism for a football team . One ought to read . "The English football team is playing the Dutch team" ( or would you advocate the Holland team ) . If you wouldn't say Holland team or Denmark team then why would you say England team? The fact that everyone says something wrong does not make it right. This anomaly has crept into the England language, created by journalists for their own slick ends and people like yourself have forgotten what is actually correct. As far as Liverpool is concerned , you are right because Liverpool FC does not represent the city of Liverpool and it is therefore just a name . As far as Arsenal is concerned there is no adjectival form. Your point about not all supporters of England's national side is probably the reason why this anomaly was coined in the first place. When English fans behave appallingly abroad the use of England fan is an attempt to mitigate the damage done to England's reputation( or is that now the England reputation? ) by inferring that the supporters were probably not really English. Scottish supporters are Scottish and proud to be called so.

I am British and yet I fully concur with the Americans . England or any country ought to be used in the singular , after all the players are representing their country and more importantly the word is singular. It is indeed painful to listen to " France have just scored a goal" . This is not only grammatically wrong but it is also illogical as only one of the French players has just scored a goal. Why , therefore, doesn't the commentator just say this.
Never understood the use of "England supporters" either . Surely, they are English supporters or supporters of England. It becomes even more baffling when the same commentator goes on to talk about the French or the Scottish supporters . The problem as I see it is that the news media in England have no clear strategy for maintaining good grammatical rules and the editors do not rectify the mistakes made by their journalists . Also the standard of education in England is very low with schools teaching little or no grammar leaving the common masses to learn their English from what they hear on television or what they read in tabloid newspapers.