Native is more about replanting things into a stable ecosystem, versus non native, which can become invasive and detrimental to that ecosystem
Iceland's tourism marketing department is super impressive; I see a barren rocky hellscape (I've been there twice, both times as emergency layovers due to XYZ airline problems) but people who buy into the ads consider it "beautiful and otherworldly", I think, because there are no trees there besides the ones planted in the cities. The bus trip from the new airport to the capital is about 30 minutes, other than Craters of the Moon national park in idaho I don't think i've seen a more barren stretch of land, especially so close to a major population center.
There's nothing quite like hiking for miles before looking down and realizing that you've been walking on a dense two-dimensional mat of berry bushes and spiral-shaped alder trees. It's quite possible that you saw trees but did not recognize them as such -- from a distance, this "flat forest" looks a lot like moss. Not much can survive annual meters-deep snows, which is one of the reasons I'm uncharacteristically flippant about invasive species (the other reason being the sheep population).
However yes the ride from KEF to RVK is particularly barren looking.
AFAIK the main factor in those "harsh conditions" is sheep farming. Sheep on Iceland are kept pretty much without any fences. They will eat saplings and small tees. There is an amazing photo somewhere of a little island in a river that's in essence covered in forest. Everything around it is mostly moss as you call out.
Another factor, especially on the Rejkyanes peninsula towards the airport is that this is also a very young part of the island. It's mostly still lava rock. This isn't representative of other parts of Iceland.
Source: visited 5 times and travelled the island extensively.=
But, to be fair, if your measure of a fertile landscape is a forest then those are relatively few and far between. Personally I tend to feel a bit claustrophobic when there are trees boxing me in on all sides and I can't see the mountains. :)
