The philosophical question here: is a stereopair of 2 near-orthographic (near side general Projections still a projection, or is it only a globe, if it's tactile?
In general I would prefer the CanvasRenderingContext2D way to handle this simple display use case, since it looks cleaner and more predictable across devices on screen and doesn't keep your gpu busy when not animating anything.
But it's perfectly possible to create geodesically-correct buffers, for example - such as you might see when calculating ballistic missile range over thousands of kilometres - in a 2D projection, and indeed this has been available for decades. And we have plenty of global models, such as WGS 84: https://en.wikipedia.org/wiki/World_Geodetic_System
So what exactly are you talking about?
...as datasets based on 2D map projections.
And different places have different projection systems.
2D projections will be with us for a long time.
In essence:a patchwork of local references frames per plate is prefereable to a single global one, when having to work with measurements over the time of decades. Which happen to also work reasonably well in 2D when projected.
https://www.openstreetmap.org/user/StephaneP/diary/390290 https://news.ycombinator.com/item?id=20460596
So you need a projection to map the surface data onto a sphere and another one to map the sphere onto the 2d screen. No way around it. Using the same projection for display as for data saves a transformation. Usually it is some variant on Mercator because it is the one people are most familiar with.
In the end unless you are starting to think about true 3D (multi-story buildings, caves,...) thinking of a "3D globe" is just a bit of projection math that doesn't fundamentally change the problem.
I don't want to upset you, but I really think you are not speaking from a position of knowledge if you think otherwise (I have a couple of degrees in Geography including one in GIS specifically, plus 15+ years' experience in the field).