Iceland should make up its mind. Flights to Iceland (from pretty much anywhere) are extremely cheap, presumably due to some sort of Icelandic tourism-board subsidy. This attracts people who choose vacation destination based on price... who might not be the most motivated to nurture (or even pay attention to) the local character of the place they visit.
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.