Stable Diffusion for example. Why train it on "ugly" pictures? Why not train a model on only the best and most awarded pictures with the best artist? wouldn't the final output have an overall better quality, instead of averaging in with "lower quality" pictures.
My take is that "good" pictures are not enough. Models like Stable Diffusion need a lot of data for training.
Every picture helps the model to gain a deeper internal representation of images, and their relation with the provided caption and every single word in it. For example, LDM (on which Stable Diffusion) is trained on LAION dataset, which has 5 billion image-text pairs. And the autoencoder component was also pretrained on another huge dataset.
Having so many images helps the model to differentiate each context, and to represent the huge variety of concepts it can currently generate. It could also learn an internal representation that separates in some way "good" and "ugly" images.
"Good training data" does not refer to if the image is of a particular artist or resolution. Rather, "good training data" refers to data being curated to match the use-case.
I'm confident Stable diffusion have had some kind of curated-quality test, for example on not training on a 100% white image.