Recongizers are often used only on inputs from some nontrivial distribution (e.g. image models on actual images and not white noise). You need a model for that distribution to use a discriminator as a generator.
Compression is ~equivalent to a model of the thing being compressed in a closer sense than that for recognizers. It's just often not that good of a model, because, among others, runtime performance of decompression is a consideration that at some point overrides optimizing for smallest (expected) compressed size.