One possibility is that I've noticed that in old publications (mainly British but some American) from before about the 1950s, prefixes smaller than micro weren't used at all. Very small capacitances were labelled as uuF (micro-micro-Farad, i.e. millionths of millionths of a Farad which is equivalent to a picofarad). For values around the nanofarad values, it seemed to be a matter of preference or house style whether to label a capacitor (or should I say condenser!) say 1000uuF or 0.001uF. (I'm using u for the greek mu because I'm not sure how to get a mu symbol here, texts of the day would universally use mu).
Maybe when pF became more accepted, designers simply replaced uuF with pF, but were already used to there being no equivalent to nF so felt no compulsion to use it. In Europe where metrication and the SI units and prefixes were being adopted more rapidly than the US, perhaps we accepted nF more readily?
All speculation, but plausible maybe? I don't buy the n being confused with mu explanation - surely in scribbled handwriting, p is more easily confused with mu?
I expect the reason we associate this phenomenon with capacitors is that they are the only common component where pico- and nano- sized values are regularly used.