Farmers certainly understood you could breed for traits, and so did professional breeders, including "fanciers" in Darwin's time. Artificial selection by pigeon fanciers was one of the many influences for Darwin.

But artificial selection is not evolution, any more than the fact that ten thousand years of dog breeding have still produced dogs that can interbreed — they are all the same species, and can even interbreed still with their non-domesticated ancestors. So artificial selection, while giving some bold examples of how malleable the forms of plants and animals can be, was not obviously answer to the "species question" — how different species came about in the first place.

What you are getting at, at its base, is a question of how does heredity work, and that is certainly core to evolutionary arguments. Darwin himself did not understand this, but presumed there must be some occasional source of innovation that allows a dog to become something different over a very long time period. It would take until decades after Darwin's death for a better understanding of heredity to come around, though.

Today we look at artificial selection and very easily make the Darwinian jump: that nature itself does something similar, and that over very long time scales you could end up with evolution. But this was not intuitive to people who a) weren't used to thinking this way anyway, and b) did not believe that life had existed on the planet as long as we now know it did (even for Darwin, the latter was a big leap, and even he didn't imagine a -billion- years of evolution taking place).

There is no reason whatsoever to expect that farmers, pigeon fanciers, and the like spent a lot of time speculating about "what would happen if you did this for a million years?" — again, this sense of "long time" was not common, and was only just becoming a possibility in the 19th century, with the discovery of new fossils, of geological evidence for long periods of time before humans, including ice ages, and so on. These debates about time were a major part of Darwin's inspiration, context, and reception.