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.

What do you think about the suggestions in the article for why this isn't ideal?

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)