Now, if the song is about really affluent persons (in 1962), as Jeri confirms, why would they live in prefabricated houses of shoddy material?

I think we can read too much into one word, at least when that word is "ticky-tacky". I don't picture the houses the song's describing as cheap or shoddy in construction. It's more that they will have been thrown up quickly, designed for show rather than architectural merit, and all with the same lack of taste. As I understand it, the point of saying "they all look just the same" is precisely that they aren't meant to look the same - they're each designed as somebody's dream house, but they all look the same because all these people are having the same dream.

It's actually much easier to answer the question about building materials in the Chilean context. Victor Jara didn't translate the "all look just the same" line directly; his version says

Las casitas del Barrio Alto,
Todas hechas con recipol

Or:

The pretty houses of the rich suburb
Every one made with Recipol.

Quoting a poster on the Word Reference forums:

"Victor Jara is speaking about a constructive technique used in the richest suburbs of Santiago involving a core of expanded polystyrene, covered with a metallic grid and concrete that allowed for an extreme control in the shape of houses, but that was extremely expensive in the '70s, since it involved, at the time, importing all the polystyrene and paying high importing taxes. This fact alone restricted this constructive technique to those suburbs. "

So there you go - modern, light-weight construction techniques, making it possible to build large houses with unusual designs, were being used by the Chilean 1%. Their houses were made of ticky-tacky, but it was expensive ticky-tacky. But I don't know if anything similar was being done in the Californian outer suburbs that Malvina Reynolds originally wrote about.