It's not at all clear it makes it easier. My great-great grandfathers children and the children of his brother have different last names. That's before dealing with the hassle of married names vs. maiden names for the women.
Most of my family is in Norway and Sweden, and used pretty much the same method as Iceland, except to throw an extra wrench in, a lot of the time people would either use the name of the farm they were born on in addition or or instead of the name derived from their father. Since that could often include extended family, and different owners over time, there might be a proliferation of people with the same last name as you with no close relationship, while someone with a completely different name might be your first cousin.
My last name only exists because one of my ancestors got tired of the name confusion and renamed his farm (changing one letter) because the local area were full of people with the same last name on farms with prefixes like little/large/upper/lower to separate them all, most of whom are not closely related to us due to purchases (the exact same change has happened two different places in Norway; as a result about 50% of people globally with the same last name as me are relatively closely related to me - the other roughly half we've not found a connection point to, but of course one will exist far enough back).