In my experience, the networks with fully connected networks are restricted by their input image dimensions. Change in image dimensions will result in input to the linear layer having different dimensions. This will throw an error. The fully convolutional networks are designed for this problem of handling multiple image sizes. Because not all data can be resized to the expected dimensions. Imagenet the dimensions are restricted by 224 * 224. It is because of fully connected network only.  But in general available datasets will have fixed dimension. So the model can be saved for that specific dimension. Resizing is generally done for classification tasks. Padding is also an alternative.