It's interesting to wonder what they'd gain from it. Given just the geographic distance, would it really affect things like trade, movement of people or security cooperation.
My understanding is that they're stable since the financial crisis.
"Stable since the last crisis" is not very convincing. In the EU they would enjoy lower interest rates, a more stable currency and voting rights. The last bit will help negotiations about trade a lot.
If you're going to adopt the Euro to get the benefits of improved trade with the rest of Europe, you might as well join its trading bloc and get votes on its regulatory bodies at the same time...
There are pros and cons to that. The euro isn't just about trade, it means your own government cannot manipulate currency (see the banking crisis) and may bring better interest rates.
I'll admit to skiphing section that discuss details that don't interest me but I did't find them.
in any case nothing is ideal anyway. The question is what set of pros and cons are the best compromise. That is something for the people of Iceland to answer not outsiders like me (and perhaps you)
I wonder if they could benefit from CO2 emission controls.
Iceland's energy is highly renewable (hydro, geothermal), and they have substantial potential for mineral carbonation of CO2. Mafic rocks like basalt, particularly with high olivine content, are close to the top for targets for conversion of CO2 to carbonates.
Iceland is already part of the EEA and through that, joined the EU Emission Trading System.
Carbfix, the company doing the mineralization stuff, is already receiving quite substantial funding via the EU Innovation Fund, which distributes ETS income to innovative climate technology projects.
Iceland could leverage geothermal energy to produce green forms of ammonia or hydrogen. Not a jackpot but strategically it is fairly inexpensive to leverage. The EU doesn't have a good alternative to cheap Russian gas at the moment. The price of natural gas in the EU is about five times the price than in the US.
Blunting the Common Fisheries Policy would be a significant benefit - they need to abide by as part of the EEA, but can't change decisions surrounding it.
Also opening EU funding opportunities for plenty of infra enhancements.
My understanding is that they're stable since the financial crisis.