It hasn't always been the case. The Icelandic legislature - certainly up until the Kreppa (crash) - was notorious for its links to big business, banks and especially the fishing industry. In such a small country, there's a very high chance that either you are a blood relative to, through marriage, business partner or school friend of someone who would appreciate favours when you get into power.
There has been an unhealthy concentration of power in Iceland, called 'The Octopus'; first amongst fourteen families (most with fortunes built on the fishing quota distribution) and then by three big corporate entities run by just three families. Björgólfur Gudmundsson and his son, Thor Björgólfsson ran the Landsbanki bank (remember IceSave???); Johannes Jonsson and his son, Jón Ásgeir Jóhannesson ran Baugur, and Íslandsbanki (later renamed Glitnir); and Lydur Gudmundsson and his brother, Ágúst Gudmundsson who had major shares in the third big bank, Kaupþing.
All of them knew one another very well, all of them had business interests with the other and some of them had borrowed money from their friends' banks to build their businesses. So when one business failed, the hugely leveraged corporations built around them also collapsed and that took down not just one, but all three of the major banks in Iceland.
And who had been running the Central Bank of Iceland that was meant to prevent this sort of thing? One Davíð Oddsson, previously been Prime Minister for the conservative Independence Party. When it was clear his position at the Bank was untenable, a friend appointed him editor of the main newspaper Morgunblaðið despite no journalistic experience. There, with the backing of the paper's owners, he forced huge numbers of resignations, but used that position to attack the coalition government that was trying to put the country's economy back on track after his mismanagement. He did a good job as the coalition lost the next election and - the Independence Party got back into power and started the same old policies again.
Davíð then went for the Presidency, but fortunately he was beaten by the current holder Gudni Johannesson.