(Primo Levi's 'Chromium' in 'The Periodic Table' has several great examples of the way solutions to old probelms hang around even when the problem not longer exists.)
I have seen readability expressed as another reason for double-spacing. It's not easy to track down the evidence for this. Kruk and Muter(1984) report "single spacing produced reading that was 10.9% slower than that produced by double spacing" on a 'video' screen. Weller (2004) reports on a previous study that "It was discovered that single spacing of text requires more eye fixations per line and therefore fewer words are read per fixation, which increases reading time (Kohler, Duchnicky & Ferguson, 1981)." But Mills and Weldon (1987) report that this same study showed a 2% slowing of reading rate, hardly convicing evidence.
Other writers express the view that this convention is out-moded e.g. the author of the Tex manual : link
Princeton University now accepts single-spaced printed copies although ProQuest (an online dissertation repository) still requires double-spacing for the electronic copy ( and hence all printed copies therefrom). It is claimed that this improved on-line readability.
A PhD Student in the US has calculated that 20,000 reams of paper would be saved if ProQuest accepted single-spaced.
Double-spacing is often mandated in legal practice but even here the convention is challenged.