No, it is true that eventually most branches will end. It's just on the timespan of 3000 years, 80% of the population will likely be a common ancestor. But if you extrapolate back far enough, there will be one and only one. The only way branches can survive forever is if you assume that all genes have essentially the same chances of survival. This obviously isn't true. Even the smallest enhancement will quickly spread throughout the population.

I am curious when the most recent unique common ancestor of humanity existed. Would we consider him human now or something in between?