Well, obviously nobody can ignore a global nuclear war. The thing is, though "Space Seed" asserted that the Eugenics Wars and WW3 were the same, after "Encounter at Farpoint" bumped WW3 to the mid-2000s, most of us assumed that the EW and WW3 were actually two different wars decades apart -- which allowed for the possibility of 1990s Los Angeles in "Journey's End" being unaffected by a contemporary EW happening elsewhere in the world. It wasn't until SNW came along that they were reintegrated into a single war that took place in the mid-2000s, which compels a new interpretation of "Journey's End" in which, indeed, the EWs weren't happening (and the DY-100 ship depicted in Rain Robinson's office was not used as an exile ship in this version of history).
You're entitled to think that, but you're just one person. The creators of a work of popular fiction have to make it appeal to a wide range of tastes, not just a single person's tastes. The goal is to make it easy for new viewers to get invested, to build on-ramps for them instead of barriers. And making the show's version of the present more familiar to the viewer is such an on-ramp. It smooths out what could be an obstacle to entry for some, even if not for others.