I've hit this on a few wikis where, for some (at the time inexplicable) reason, I'd get only the crappy Fandom wiki with above queries, and a good wiki when searching only for "<game> wiki" after seeing a link to it on reddit.
When the reason is to move away from Fandom, get people what they are looking for, and perhaps attract contributors, this is an issue. Your average gamer won't route through the Wiki's main page, rather rely on the top Google search result for their issue.
There's a ton of historical evidence of wiki migrations (1) starting out with all of the editors and none of the readers, (2) not doing anything to get those readers to the new site, and (3) ultimately losing the whole war because the reader->editor flow was still happening on the Fandom wiki. "Invisibility" is absolutely not desirable here, even if your only goal is maximizing the amount of good contributions.
So yeah, when my goal is to search for content that would be in a wiki, I'm ecstatic when I get an independent wiki over fandom. The Google Jail is the opposite of what I'd want.
Nowadays, I use Kagi which is better than Google but it's still not to the level of Google in 2010.