Anti-aliasing techniques are common elsewhere in 3-D graphics, and can be used just as well in light-fields.
Rendering for 2D and display are two different beasts -- but I'll own the fact that I'm not formally trained in this and there may be subtleties -- or even obvious signal processing facts -- that I'm getting wrong. (But if I'm wrong, I'd love to know how, for my own edification.)
It doesn't need that at all. Light fields can be interpolated like anything else, just like bayer filter for color on camera sensors or 4:2:2 color compression on the signal side. But if you're doing 3-D rendering, you can match rays exactly to your distribution on the display if the renderer knows the distribution of rays on the display.
Interpolation is always going to reduce quality, but it's better than aliasing, so there's going to be a trade-off analysis that needs to be done. I don't know what the results of that would be, so this is all theoretical.
Furthermore, if you're interpolating rays, you're necessarily not doing what you originally proposed, which is to only light up a (random or pseudorandom or evenly distributed) subset of the pixel display elements, presumably to save on rendering cycles.
Let me just say, more generally, that intuition trained on 2D doesn't apply directly to light fields.