What?! How can you both be so shallow on your analysis?
First of all, I urge you to find any actress that performs that role (or another one similar) nearly as great as she did. She embodied the character so well, showing the audience her deepest emotions: her imprisonment, her isolation, her lack of sociability due to the low acceptance she had on the island. She was so big that she even strenghtned the other actors/perfomers appearance. She actually shows, by her acting, the natural incompatibility between her and the environment where she was dragged to.
Moreover, even if you don't see her magistral performance, there are two additional things that she contributed to and that made this film so great.
The first one is definitely the story and its symbolism. You have the natural kind of story of post-war Italy, which revolves around the famous neo-realism from that period. Not only Bergman is great on this aspect, but also the way Rossellini handled the story makes the film greater than what it would have been had the director been someone else. The island represents the isolation: she is taken there, hoping to be going to somewhere where she can meet new people and build her project of life, and she finds a small, deserted and mid-destroyed island. For someone used to live like a "lady", someone with wishes, ambition and demanding a certain life style, it is perfectly normal to behave the way Bergman portrayed.
And what about that volcano? It is kinda like her husband, who both attacks and imprisons her, waving in a "character" of continuous rage and fear.
Then you have the other symbolism: the fish trapped, the population evading the eruption by going to the sea on the boats (and then returning to the island to continue their daily lives) the eruption when she tries to run away from there, by trying to reach the other end of the island - this is all part of the mise-en-scene that is extremely important in order to understand her performance. This film is full of symbolism and Bergman fits so perfectly on it!
The other thing you cannot forget is the directing itself. How many filmakers can you imagine doing such a perfect and antological scene like the fishery one? And the eruption? And Karin evading in the end? He actually gave life to the volcano and the island, which actually helped and strenghtned Bergman's performance.
I'm sorry, but how can you miss all these things? I mean, it is okay not to like the way she acts. I can deal with that, it's perfectly natural. But saying that she was "annoying" or "whiner" is completely off-base. Believe me, you have got to have seen more from the film that just a fool woman dragging herself around the walls of her house.
Compared to her performances in her previous movies, she is whiney, indeed. But it was a labor of love for Ingrid, since she left her husband for director Rossellini. And love makes actors do strange things, like eat the scenery like it was- stromboli.