Yes, super sampling is a valid way to do antialiasing. But as you already mentioned - it will be much more expensive because of 4x more work needs to be done. And that can be pretty expensive when you have complicated fragment shaders. For HandmadeHero game this could work fine, but for complex 3d games this will get very expensive.
And if you will want even better picture - 6x or 8x? The cost for that will be crazy. 8x means 64x more pixels to shade.