I made a voxel engine without using Three.js a few years ago[1] (well, the engine is rendering-agnostic, so I actually used Three.js, but only the really basic primitives, such as BufferGeometry).

The issue wasn't so much WebGL performances (especially since WebGL is actually hardware accelerated), but rather the CPU cost required to rasterize a real-time voxel world into a polygonal geometry. I wasn't able to generate geometry chunks fast enough to match the player speed (so the player was always able to catch up with the rendering). Even using workers wasn't improving the perfs so much (but I think could have improved that by changing the update heuristic a bit).

But it was pretty fun nevertheless! I'm proud to be one of the few JS voxel engine using marching cubes, which look much better than usual cubes :)

[1] http://arcanis.github.io/voxplode/ (may take a while to load, may be a bit buggy, especially if you move before the chunk underneath has been loaded)