I had my first bought new bike when I was 11, in 1963. It was a sit up and beg Raleigh adults bike (I was 5' 8" with about a 28" leg so the bike size would have been to suit that) with straight handlebars, Sturmey 3 speed gears and cable brakes, so even if they were still using rods they were certainly also using cable by then. (Also steel rims so the mechanics were irrelevant in the wet, the brakes might as well have not been there.)
As for cotter pins - I missed out on their demise, as I had one bike from the mid 70s to mid 90s, and during that time they vanished from new bikes.