[Geimfari]

Flights to Iceland are cheap because the airlines' business model is being a hub for cross-Atlantic flights. Later on, advertisers started marketing towards those who were already crossing the Atlantic, encouraging them to spend time in the country since they were already there.

It would be possible to tax tourists more for their stay, limiting low-value tourists. It would also be possible to just put a hard limit on the number of visitors, which to me sounds like a reasonable solution, as no country can handle this growth in visitors in such a short time.