>Which is an incredibly specious conclusion because when would the gut fauna ever be wiped out?

It's called "gastrointestinal illness". From the article I linked:

"Research in 2012 reported that individuals without an appendix were twice as likely to have a recurrence of Clostridioides difficile colitis. The appendix, therefore, may act as a reservoir for beneficial bacteria. This reservoir could repopulate the gut flora following a bout of gastrointestinal illness."