Vacuum tubes were a mainstay of digital computer technology until around the 1960s, where transistors (and later integrated circuits) replaced them for most applications. In real life history, one of the last commercial tubes to be developed and widely manufactured was the nuvistor, a small, relatively reliable tube used in radio equipment and televisions. The linked Wikipedia article has photographs of the tube, which has a metal casing and is about 11 mm in diameter.
In a hypothetical setting where the invention of transistors and integrated circuits were delayed indefinitely, how much smaller and more reliable could 'traditional' vacuum tubes operating on the principles of thermionic emission been made, given sufficient commercial demand for further innovation? What limitations (heat dissipation, fundamental physical effects) might come into play that would prevent tubes from shrinking beyond, say, the size of a grain of rice, or a grain of sand?
(I'm aware of the existence of nanoscale vacuum tubes, but these devices are fabricated using the same photolithography technology invented for manufacturing integrated circuits, and for the sake of this question I'd like to exclude them, or anything else that relies on semiconductor technology or technology developed as a direct result of semiconductors.)