That's right, it's not like that. Nintendo sues when they know they can win, as in the Yuzu debacle where keys were extracted and distributed in order for the emulator to work. There's nothing like that necessary for NES, SNES, or even (as far as I know) N64 or Wii. So no, Nintendo would not sue.
Dolphin ships with a bunch of keys in the source code[0]. So do almost every other emulators for any console from 6/7th gen consoles (ps3, xbox360, gamecube), see delroth's post on the matter here[1]. It's really not that simple - jurisdiction matters a lot, and also Nintendo's own priorities.
Nintendo will not need to sue because they know that the only way Apple will ever allow a NES, SNES, or N64 emulator is if Nintendo publishes it themselves and offers their own games for it through IAPs.
There is more money in having Nintendo be happy to support iPhone platform with games than having them feel insulted over a low revenue app that is also on the platform.
Nintendo generally leaves the retro, unsupported console emulators alone. mGBA, Project64, Dolphin (except for their request to take down their steam page).
Case in point: there's an endless list of Nintendo system emulators on the Play Store, many of which have been up for years with no issues. I'm sure Nintendo would prefer they weren't available on there, but as long as they don't distribute any copyrighted files or keys Nintendo can't really make a compelling case to Google that they shouldn't be allowed.
Thanks to the DMCA, they wouldn't need to make the case to google, just send a notice and they're obligated to comply. The dispute would be between the uploader and nintendo once a takedown is sent, and maybe counter-claimed.
An NES emulator, for example, would not require the inclusion of anything copyright protected, since there is no built-in system program code. An NES emulator app could instead offer the user to manually install games in the app sandbox, like ScummVM does today, with no concern for whether they were obtained legally or not.
