I am not saying split England into different countries, but split regions into federal districts. That has nothing to do with separation of England, does the USA send states to the world cup? I don't know what you are saying there.
Growing up, I had absolutely no problems comprehending that my county (cumbria) was part of a region (the north-west), which is why we got Manchester's news on the TV. That region was then part of a country, and a few countries made up our nation.
We already have these tiers of identity. We already have borough seats, county seats, city seats, etc. If we federalized the UK along the same sort of regional identities the BBC does, I don't believe we'd suddenly lose any county/country/national identity.
(Perhaps not exactly the same boundaries, but I can't help looking at their map and thinking - yeah, that's a good start)
It's less of a problem for the Germans because they are comparatively more invested in europe, for example using the currency.
If you want to keep sending an England team, keep sending an England team. Big deal.
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.
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.