by allstar64
In my groups experience, winning without taking any islands against good players in the game's current form is very very difficult if not impossible.This really comes down to two things. First of all, islands overall have much much better payoffs both in income and in bonus than the home board especially as you fill up more and more of the home board. Players investing in islands often will easily surpass the income/bonuses compared to players focusing on their home board.
The second issue is, its pretty easy for good players to just fill up their home board with tiles to spare so without an island you'll have a bunch of tiles sitting around doing nothing for you. Islands are a good way to turn those extras into vp. The only other option is houses but they are often weirdly shaped making it difficult to utilize your pieces efficiently.
Players who avoided islands would usually struggle to break 100-110 unless they got some sort of really good emigration strategy working. Thankfully the newer islands have relieved some of the pressure on islands by expanding the number to 6 meaning taking islands has become more about whether or not they are the right move for the given moment and less about being afraid of being closed out of them.