Operators typically bring fiber close to homes, while still using DSL for the last mile. True, this requires investments, but not much compared to wiring each home with phone lines, cable, or fiber (all of which have been done before).

Note that part of the reason that cable is able to reach such high speeds is precisely because they use the same infrastructure I described: fiber to the neighborhood, then coaxial cable for the last mile. I don't see why DSL operators shouldn't be expected to do the same if they want to compete.

I think it has less to do with density than with willingness to invest in upgrades.