Why did this trend come about?
For developing websites there are three major approaches toward how they are developed*:
- Responsive Web Design
- Adaptive Web Design
- Separate "Desktop" and "Mobile" sites
Responsive Web Design (RWD) is where a site is designed in a way that it changes to fit whatever screen size it is rendered on. From a technological standpoint, media queries are often used so that the site changes automatically. For example, what might appear as three columns in a wide browser window could turn into a single column when the window is narrowed.
Adaptive Web Design (AWD) is where a site is designed in a way to use different features or different content for different devices. From a technological standpoint, media queries may be used, although they tend to depend on the actual size of the screen rather than the current size of the screen. Often device detection is used as well to change behaviors. For example, what might appear as three columns on a laptop with a wide screen could be rendered as a single column on a smartphone with a smaller screen.
Separate sites is where the server (and sometimes client) changes which website is rendered based on the device that's making the request. From a technological standpoint device detection is often used along with some other indicators, such as query string values to override default behaviors. Additionally this is what leads to the
m.example.com URLs when viewing/linking to a "mobile" site instead of a "desktop" site.
should you still do it?
This question starts to be opinionated, and different people will have different opinions as to what the right behavior is.
My opinion is that RWD is the correct approach for the majority of websites, with AWD being appropriate for some applications, particularly where features are significantly different** such as with a keyboard and mouse compared to a touch screen for a drawing based web-application.
If you're using RWD, the content and feature set should remain identical (or at least congruent) and given that there is no separate mobile site, it is impossible to link to a "desktop site" because there isn't one. It's the same site.
If you're using AWD, the content and feature set should remain similar, but in some cases it may be necessary to provide a means to access the "desktop" experience. Feature detection can only do so much, and you may happen to use a small touchscreen device that has a keyboard and mouse where you want the "desktop" experience. In these situations it's appropriate to allow the user to toggle the behavior. This may not mean an actual link to the "desktop" site. This may be simply allowing a toggle between touch screen controls and keyboard/mouse controls.
If you're using separate sites, it is appropriate to allow users to toggle between which site they're viewing. Not allowing a user to view both versions of a site starts to enter into legal grey areas as well. Consider an article that has a sidebar that lists open job positions. If that sidebar is only rendered on the "desktop" site and you don't provide an equivalent listing for the mobile site, mobile users could claim that you're discriminating against them.
Links to "desktop" sites are only necessary if you actually have a difference in content and functionality between "desktop" and "mobile" versions.
If you don't have two sites, and you're not hiding/showing content to users on different screen sizes, then there's absolutely no reason to use such a link.
* Be aware that there is no standards body to govern the exact meaning of the terms I'm using, so you may have differing definitions or use different jargon for the same concepts.
** although it's possible to combine the two approaches