The light is produced by electrons combining with holes, so the size of the material doesn't come into it (unlike an antenna). I've personally pushed* a single rubidium atom about in a quantum computer and watched it move by emitted light (rubidium atom: ~0.25nm, emitted light 420nm depending on excitation).

* Ok, actually pressed buttons that manipulated the electric field that was trapping the atom and watched the result on a display - lot of physics going on behind the scenes.

Something akin to reciprocity still applies, no? You have a tiny rubidium atom, way too small to couple particularly strongly to the electromagnetic field at visible wavelengths. So it has a low cross-section for absorbing visible light. Won’t it necessarily radiate rather slowly as a result?

I would expect this to be somewhat of a problem with tiny LEDs. In an LED, you inject electrons and holes and you hope that a magical quantum process happens in which an electron and a hole meet, annihilate each other, and emit a photon. But this process is slow, and the electrons and the holes may wander around for a bit before combining. But in a very very small LED, smaller than the mean free path, I’d imagine you might have an issue where the electrons and holes frequently make it all the way across the device without recombining and manage to lose their energy as heat when they hit the opposite electrode. (I have not drawn the diagrams or checked the math here.)

(I took the relevant classes in grad school, but I’ve never done this sort of work academically or professionally, so no promises that I’m right.)

It's probably more impressive that the LED was manufactured with light photons. I know it's "normal lithography" problems, but making a 500nm device out of 300nm or 400nm waves of light is downright impressive.