The other common reason I use "show desktop version" is when the mobile "version" displays nothing but "use our app", while the desktop version actually provides the content.

I've had to use this a few times when on my phone to be able to actually access the webpage.

Many years ago, there was a trend to show a different website, sometimes on a different domain and often with more differences than just a mobile version of the stylesheet. Sometimes the mobile version was not updated enough, or there was a reduction in functionality, hence the paranoia.