Students should be primarily shown a globe. A physical one, if possible!
In fact, paper maps in study books showing a large part of the world should also be accurate 3D projections.
But there is no such thing as an 'accurate' 3D projection onto a 2D space is there? What do you want them to do?
If you have a world paper map, though, there's no real way around inaccuracies. You can trade off one inaccuracy for another, is all.
And even for systems that do adjust the projection based on where you’re looking, such as Google Earth, that simulated globe is still... just a projection. It’s got the same issues in that areas and sizes are distorted.
Now you have to click a button to turn it on: https://old.reddit.com/r/GoogleMaps/comments/eoav6s/did_they...
I think the point here is that it is interactive and can be made as accurate as you want by moving around, zooming in and looking at the center. Not at stuff at the edges which might be distorted a bit, because yes, it's still a projection. Go to Map Style and enable gridlines and then try to argue it's not accurate.
Of course, rendering a globe in WebGL or whatever and drawing it on a 2D screen is still a projection, and it still introduces distortions in shapes and areas, but the 3D-ness of it gives your brain the cues it needs to "correct" the distortions.
It clearly doesn't - you can zoom out and see this for yourself. It uses an equatorial variant of the Mercator projection.
https://i.imgur.com/D6fMLop.gifv (Native vid: https://i.imgur.com/D6fMLop.mp4)
As for whether it looks "so bad," it's hard to tell from that video, because it's a small segment of the map, all in the northern-most latitudes.
The Mercator projection is very shape-conforming (except close to the poles, as you can see from the huge top of Greenland), and its size distortions depend on latitude, so locally it's always going to be very "good" compared with a globe. You're not going to see any huge "errors" just comparing the before-and-after shapes of Greenland (although, again, the top of Greenland is very distorted there), or comparing its size to its closest neighbors.
The first frame is the Mercator projection; the whole conversion (See GP: "..I think any digital map that lets you zoom out more than a hundred miles or so should be an accurate 3D projection" and then the reply "I think Google Maps already does this at least") is about now on GMaps you can enable "globe" option, which uses a more accurate 3D projection.
The video shows before/after enable globe option.