-In Fallout 2, there's at least one fully-operating car (the "Highwayman")

-In Fallout New Vegas, we learn that the NCR have operating railroads (Powder Gangers were convicts that used to build/maintain railrods, and there are NPCs mentioning mining rocks that were taken away by train)

And still, caravans travel on foot mile by mile, in a dry desert landscape, no less. Surely, when a Brahmin can be used to carry packs, it could also haul a cart? There is wood available, and iron, and when railroads and trains can be maintained and operated, surely a Brahmin-drawn cart is well within the technological abilities of the society? And where have all the horses gone? It really makes no sense to not have horses, when other pre-war animals exist, albeit in mutated variants... Even if horses had somehow mutated to no longer be rideable they surely could be made usable to haul carts or carriages?

One, the horses, can be explained by artistic choice. Horses being used as transport are pretty generic and the devs want to use something a bit more post-apocalyptic feeling: ergo we have mutated cattle being used for the same purpose. I agree it makes no sense though why horses should not exist. But there's a lot of animals that don't make an appearance in the Fallout series.

The other can be explained by engine mechanics. Its harder to animate a moving brahmin and cart successfully than it is to just strap a back to one and call it good (https://www.youtube.com/watch?v=L3BgAMH6Qp8). In New Vegas you can see usable carts everywhere, so its beyond question that carts are being used in-lore. A similar case can be made for trains. We don't see them, but we know that steam trains are used.

Does it specifically say steam trains? All the trains shown in-game in New Vegas are diesel (EMD F-units, unless I'm mistaken - or at least very closely based on them).