As a sovereign nation, the UK has virtually limitless freedom in deciding its internal structure. You can pick and choose which things are decided at which level, and how different subdivisions might be grouped into higher levels for some purposes but not others. You are not required to follow any established model -- and you are certainly not required to follow the US's rigid structure.

If you want to keep sending an England team, keep sending an England team. Big deal.

Germany doesn't send Saxony and Bavaria to the world cup.

As I noted in a different comment: The current situation of an England team is an historical oddity: England, Scotland and Wales are considered constituent countries of the UK. Only a handful of countries worldwide have constituent countries, and the exact details of in what context they are treated as countries vary greatly.

But if the UK was turned federal, there's no reason why the new federal entities would be considered countries any more than e.g. the states of Germany are, even though in the case of the states of Germany, many of the states still closely match countries with a long history as independent states.

Sure, it's workable but how people would feel about it is another question. It would probably transpire that the countries of Wales and NI would both map directly to states with the same names (with powers). You then have a country of England (with no powers) broken into constituent states (with powers) and the whole thing starts to look like a CGP grey video.

Historically, Germany is quite different to the UK for obvious reasons. I also suspect Scotland , Wales etc would be more likely to table flip when dealing with a UK parliament than say Saxony would.

nor do FC barcelona/Athletic Bilbao play at the world cup..heh