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> as we going back in time we meet more and more homogeneous languages - which as we go forward in time get differentiated and branch out into several languages
Which might hold some ground assuming a small, homogeneous population with a single language settling a large area. This assumption kind of works for New World extensions of Old World languages, but the settlers aren't that homogeneous, they come from different places in the Old World and New World regions within the same country have different population-origin makeups. For the Old World languages that were transplanted, this small population is not homogeneous (e.g. migrations by alliances of several tribes), interacted with other languages previously established on the territory and is often too far back in time.