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The main drawback of Generalized Linear Models (GLM) is often related to their sensitivity to noise and overfitting, especially in situations with complex data structures or limited sample sizes. While GLMs are quite flexible and can handle a variety of distributions and link functions, they may yield poor predictive performance when faced with noisy data or when the model is overly complex for the underlying data structure. This means that, in practice, a GLM might not generalize well to new data, leading to a scenario where it performs well on training data but poorly on unseen data, demonstrating overfitting.

In contrast, the other options touch on aspects that are not as critical. While GLMs can model simple relationships effectively, they are not limited in that capacity. Regarding dependence on large datasets, GLMs can perform with smaller datasets, though larger samples typically yield more robust estimates. Lastly, high computational cost is not a standard characteristic of GLMs, as they are generally more computationally efficient compared to more complex models like machine learning algorithms. Therefore, the key challenge remains their susceptibility to noise and overfitting in the context of real-world data applications.