The well method has nothing to do with autolysis, and letting the stuff sit is not a common thing. Maybe moscafj is onto something when mentioning yeast proofing, although my grandma would do this in a separate cup before making the well.
The point of the method is traditional bread making without measurements. The baker would take a large heap of flour, then make the well, add the wet ingredients there, and hand knead by adding just a little bit of flour from the walls of the well. The first, and smaller, advantage for this is that it makes it easier to avoid lumps when hand kneading. The second, and main reason to use it, is to make the proper dough. The baker would just continue working in the well, adding just a tiny bit of flour, until she had the proper consistency (which she determined by literally feeling the dough with her fingertips while kneading). She would then take out the dough for kneading on the table, or even for first proof, and would have a single cohesive lump with floured, nonsticky sides, while the rest of the flour in her container would have no dough contamination, no need to sieve. Also no leftover half- or overhydrated patches on the walls of a bowl, and a minimum of utensils to wash (which is important when you carry your wash water on your shoulder from the village well).
You can still use the method for reasons such as nostalgia, or learning to feel the dough better, but it doesn't really have advantages for your finished product in current baking settings.