People who try to maximise the chance that at least one copy of themselves will always exist will eventually wipe out those acting under the constraint of preserving continuity with their physical incarnation. I'm sure someone said something like this, but its relevance escapes me. Besides, the fact that copiers may arbitrarily outnumber non-copiers does not imply that the latter class becomes extinct. Remember also that people willing to modify their copies in order to increase 'their' chances of survival even more will in general survive even better than 'faithful' copiers. See also the works mentioned earlier.
More references welcome.
As we aren't going to agree on any of this, it would be more interesting and useful to speculate on what a world would be like in which people can upload, duplicate, and modify themselves at will. There's material here for a whole shelfful of SF novels, some of which have been written already.