I'd have thought in these days of GPS the knowledge of ICAO's would be of positive benefit if you're trying to program the bloody thing!
However, I too know them from my previous career in Flight Ops. It's rather like the phonetic alphabet, most people in Aviation know it (even if they've not needed to learn it for flying) - if you hear them often enough you remember them.
ISTR that there was an article in Pilot years ago about the coding - the only thing I can remember is Llanbedr as EGOD - the writer wondered if there was a connection with the local church!?
LL - London
BB- Birmingham
CC - Er, well Manchester...
GP - Running out of ideas now.