Hey we've got Four Corners!

The one with Belgium and the Netherlands has a park around it with a large maze, a watchtower and playgrounds.

I just noticed the map at the end is missing the tripoint Italy-Slovenia-Austria

Water, probably.

The lake is actually ~99% on Norwegian territory, it's just a tiny edge on the end that's given to Sweden and Finland. We once tried to give Finland a mountain peak though (for their 100th anniversary of independence from Russia), but the constitution states the kingdom is indivisible so the legal work was deemed too much. It would have been their highest peak if it went through.

Nothing is out there! All there is is a lake and birds and fish. ... And a wooden walkway. ... And a big ass cement block. But there's nothing else there. It's a complete void. The environment is perfectly safe!

Just made for a good border-point, really.

This is all imagined though as I refuse to recognize the sovereignty of Finland and Norway - long live the Great Swedish Empire

Seems like a non-issue to me. You'll go to whichever hospital is closest. If you're resident in one of the countries you'll be in EU/EEA and get the usual healthcare for residents of whichever country the hospital is in, if you're non-EU it'll depend on what travel insurance you have.

No worries, any of these three countries will take you without quibbling over who pays what.

exact point is probably empty. so much of matter is just empty space.