It's a matter of tradition. The four [or five if you count Republic of Ireland] home nation teams have always had separate footballing identities, preceding the very existence of any such entity as FIFA, Euro, or any such: & this separateness has always been recognised by such international bodies. It could be compromised if a UK team were to be entered for Olympics, tho that will be the badge under which other sports will be entered [if Andy Murray enters the tennis, e.g., it will surely be as a UK, not a Scotland, representative].

And, as I say, tradition is all part of it. A sort of analogy might be drawn with a popular TV quiz over here called University Challenge, in which the various colleges of the ancient universities of Oxford & Cambridge, whose colleges are recognised as part of a federal university but as having their own traditions & identities, enter separate teams; as do the colleges of London University which, unlike the Ox&Cam ones, which are small, are monolithic foundations big enough to form their own universities if they wanted; while all other teams just represent the whole of their parent university. Pragmatically, it seems to work.