Plus think of it this way, websites fight tooth and nail to stay relevant to the user. You win that fight if they "install" your app. Joining their Discord server means you have installed their application to one of the most frequented messaging apps. If this was a website, you would have forgotten about it after couple uses. At least when it is in your discord server dock, it is visible to the user and in their mind.

On of the reasons I think is their statement on making it publicly available. In order to make your images private, you have to pay a hefty monthly fee. It levels the playing field as most of the prompts are public and you can learn from others.

My guess for Discord is that it lets them offload a number of costs: from costs of hosting the content to having to develop and maintain a website

And the results are consistent with what people report on Twitter and elsewhere