Wonderful post, and I love the explanations.
Yes, cultural references can really date a book: They can let you know when a story is set (and, if writing decades or centuries later, this requires a lot of research to get right so that the story sounds and seems authentic), or, if you come across a work written in a particular era, and get (or, don't get, as the case may be) specific cultural references, this can be a way of realising that the book is of a different era, one that does not really resonate witn the "now".
Mind you, I do remember ice-cream vans - and their song - when I was a kid.
You would hear it, run in to pester a parent, and then hope (with some money in your pocket) that you could actually track down where the vehicle might be parked, your ears twitching almost like a dog's, as your short legs ran to where you hope the van might be parked, with your brother, and other kids streaming along to join us. And the thing is, I don't actually like ice-cream; rather, I liked the ritual of the van, the listening, (that music would start and stop, getting nearer or farther as was the case), persuadng parents to part with pennies, the running, the racing (I was good at running as a child, - better than my brother - and had excellent endurance, and my brother knew that there was a good chance that I could catch an ice cream van if I was with him) and - hopefully - the discovery of a parked, and waiting van.
However, the (unforgettable) scenes with the Child-Catcher in Chitty Chitty Bang Bang (a movie that was a firm childhood favourite; my brother and I saw it countless times) rather put a different complexion on my already somewhat agnostic approach to ice-cream vans; that music, those lurid colours, this vehicle inviting children to race after it......hm.