They are not "banning" emulators. They take action against two sorts of problems: leaking, and distribution of copyrighted material. Yuzu was taken down because they stupidly started charging for help with playing Tears of the Kingdom before its release. Other emulators have been threatened because they included binary console OS software (rather than actually fully emulating the console itself) or actually distributed game ROMs.

Dolphin has been around for about 20 years now. Why? Because they don't distribute copyrighted material, recommend against doing so, and don't require to include any binaries from the console.

Here's all they had to both say and adhere to, to "survive" the supposedly blood-hungry Nintendo for longer than some of the people reading this have been alive:

Where can I download game ISOs/ROMs?¶

Short answer: You don't. Buy games and dump them with a Wii.

Long answer: Downloading commercial games is illegal and thus strongly frowned upon by the Dolphin developers. To prevent legal issues, this includes gray areas like downloading games which you purchased earlier. You don't necessarily need to own a gaming console by yourself because you can buy a game disc and dump them with a friend's console. On the other hand, copying a friend's game dump is considered illegal again.

https://dolphin-emu.org/

Also, lol @ the idea that it's hypocrisy for them to use their own game files. You understand that's what a ROM is, right? It isn't magic. It's just a binary file.