The real issue is that Nintendo's Wii EULA is so vague about this subject that they can justify removing Homebrew without having to claim that it is illegal.
Technically, it's easy to prove that Homebrew is not illegal in the US (see Sony Corp. of America v. Universal City Studios, Inc.). Unfortunately, this isn't what the EULA forbids. The EULA says that Nintendo can outright disable, "unauthorized or illegal software placed on your Wii Console to ensure that your Wii Console is operating properly and efficiently, comply with applicable laws, assist law enforcement, protect us and our customers, or prevent the use and distribution of software obtained through improper channels." This pretty much means that if they decide to bust Homebrew, they can just go ahead and do it. Realistically, they probably won't because EULAs are on shaky legal ground to begin with, but they can at least begin to justify it.
Brawl+ is defensible in that GameShark and AR codes have never been successfully litigated before, despite being unauthorized hacks. However, Brawl+ does suffer from the fact that Nintendo could argue that it significantly alters the content of the game to constitute a violation of their copyright. From there, it's down to determining whether Brawl+ falls under fair use.
Personally, I think Brawl+ should more than fall under fair use, since you need to own Brawl to use it, and since some people play Brawl+ who don't play Brawl, this in fact increases Brawl's market value, so Nintendo really shouldn't complain. Furthermore, you could argue that Brawl+ is a transformative work.
ROMs and Emulators are illegal, as are WADs.
)