The benchmark suite[1] I compiled contains many different types of images. The "industry standard" sets like the Kodak and Tecnick Photos, texture packs and icons are complete. No images have been removed from these sets. Some of the other collections (photos and game screenshots from Wikipedia and those from pngimg.com) are a random sample. I did not remove any images just because they compressed badly.
Also, the fact that some images compress badly is a non issue, if the whole set of assets that you need for your game/app combined have an acceptable compression ratio. If that's not the case, by all means, chose another image format.
On average, for a lot of assets types, QOI usually performs quite ok.