A poorly made responsive layout*

If it was any good, it would be showing the desktop scaling/layout/whatever instead of the mobile when 'show desktop version' is on.

It's also not always about being on a responsive sites, a lot of places still do a m.website.com redirect when visiting the main site from a mobile device, but with no backwards redirect when visiting the mobile site (which is almost certainly non-responsive, otherwise there'd be essentially no need for the m.* site) as a desktop client - so you hit 'show desktop version', the m.* page refreshes and you just get the mobile site with funny scaling.

The website has no way of knowing you did that: this is actually Apple's fault for not changing the logical browser dimensions when you use this feature.

Well, no, it's not - it's just weirdly labeled.

Request mobile site is really only applicable to the small amount of websites that serve a m.domain.com.

Now, they could have an option to "request desktop SIZE" that would result in sites that are responsively built rendering in "desktop size" mode.

You can argue that any limitation is simply due to the feature being mislabeled, but in this case it seems pretty clear what people both expect this feature to do as currently named, and that happens to match what people also seem to want, and that would include changing the viewport to make certain you actually get the desktop site functionality.