Why are country sports teams, for example, from England, referred to as 'the England Football Team' as opposed to 'the English Football Team'?
In this context, for the name of the team, we have two options:
Consider something like "London Cricket Club". The name doesn't feel awkward, right?
Now, consider "Londoner Cricket Club". Awkward? A bit.
In this example, the name of the place (London) has been used rather than its adjectival form (and it doesn't feel odd - rather feels natural).
Now consider the opposite, wherein, by using the name of the place (rather than its adjectival form), you would sound awkward.
"Indian Cricket Team" and "Australian Olympic Team" are what people are used to hearing. If you were to say "India Cricket Team" or "Australia Olympic Team", you may sound odd.
It is what you are used hearing, that doesn't feel odd. Perhaps, you are used to listening to names of teams with the adjectival forms of the place names.
Yes, it sounds a little off.
Using 'the England team' means the one team of England.
The 'English team' has English qualities (it could possibly be the country's team but may just be comprised of English people or sponsored by people who are English).
Or there may be no intended difference, but instead it comes from headlinese, where to shorten a headline, a shorter noun is used instead of the longer adjective, 'Italy' for 'Italian', and for consistency all are given that way. AAnd since nouns can act sometimes as adjectives, this gets a pass (still sounding a bit strange).