It's a combination of GPU RAM, slowdowns (remember it's squared in dimensions), and stability (larger is more unstable end-to-end). Arguably, state of the art in image synthesis is DeepMind's PixelCNN: "Parallel Multiscale Autoregressive Density Estimation" https://arxiv.org/abs/1703.03664 , Reed et al 2017: generating 512px photorealistic images & video with PixelCNNs rather than GANs. Also good is StackGAN which does ~200x200ish but there's no reason it couldn't go up to 500x500 (just pop in a third upscaling stage).
There's far more work on GANs than PixelCNNs (see the https://github.com/hindupuravinash/the-gan-zoo ) but at least thus far, I haven't seen any GANs which appear visually competitive with Reed et al 2017's PixelCNN samples. Downside - code has not been released by DeepMind[], and you can't do CycleGAN or other stupid GAN tricks with PixelCNN AFAIK. CycleGAN is absolutely hilarious, if you haven't seen all the uses of it yet, much more interesting than generating cat faces.
[] I asked way back when and Reed said he'd try but nothing yet.
That's not it. It's easy to scale a larger image down to 224x224 and feed it into a checkpoint. And a lot of these GANs don't use such content losses in the first place because it adds complexity and makes it harder to use (have to get one of those pretrained models in the first place).
