Our son ( British citizen, but not domicile in UK) played Rugby in his boarding school (in England) . We had to get a separate insurance for him because of this. This was a requirement for all non domicile children.
I used to play ice hockey and swim when young, about 40 years ago, and despite a very similar health (welfare) system as in UK, the parents had to pay a certain, small sum, for extra insurance. One sum for the ice hockey, one smaller sum for the swimming.
This was done through the sports clubs.
School sports - no extra insurance needed.
Do not know though how they do it today.
I personally think 'idiots' like that should have to pay something volunteraly, but on the other hand, the whole idea with the European 'wellfare system' is that it should be covered, right?
I see it as a type of contract between the people and the State.
If a Brit gets wasted in Prague, and smashes up his ankle on the cobblestones in Old Town, he will get free care there.
At the end of the day, we must/should use our brains. I would love to know what those guys were thinking.