They chart nowhere. That’s not the point. Noticing that key changes are still popular at what is one of the most popular song contest in the world is however very relevant to a discussion about the public taste.
They most certainly chart in Sweden, here's the chart from May 14th (the day after the the Eurovision finals) [1]. This is "Svensktoppen", a very long-running list of top-played Swedish songs in Swedish radio. Off the top of my head, positions 1, 3, 4 and 5 were all candidates for Eurovision (and the song in position #3 was the one that competed in Eurovision).
In Swedish, this key change is generally called a "schlagerhöjning", where "schlager" [2] is the broad genre word for the type of songs that compete in the Eurovision. The term is old, obviously there's a rather wide genre spread these days but it used to be more same-same.
Edit: added a "Swedish" above, I did not realize that the chart only lists Swedish music, saw another comment mention this. Very weird of me.
I don't have the numbers but I would be cautious there. Some US music is listened in other countries, but not all of it. Not everything is easily exportable.
Also there are local musicians popular in each country. And there are musicians from countries other than the US that are international but unknown in the US.
Anyway, Eurovision is quite irrelevant in Europe too :)
Edit... for native English speakers, consider this: there're songs in which the lyrics are more important than music. That kind of music is usually boring if you can't understand what they're saying.
Anecdotally, most of the music I heard when I was travelling in South America wasn't American music. Same thing with South East Asia.
Look at the Billboard (or equivalent) charts for Germany, France, Argentina, or any other non-Anglo country; maybe 10% of the entries are English language or from American artists.
I'd rather say that what works in that huge party simply doesn't necessarily work outside of it, at least not everywhere. The ESC is still crazy successful, at 161 Million viewers this year worldwide.
At least in the UK - people are watching with a mixture of morbid fascination and ironic glee. I've never met anyone who thinks it's a valid forum for good pop music.