What is the point of listing 1000 authors for a single scientific paper?

The “point” of 1000 authors is to recognize that 1000 people contributed to the paper at a level sufficient to be considered authors, according to the standards of that particular field.

In some fields (including high-energy physics), large numbers of authors are not unusual. See e.g. the 2015 paper estimating the mass of the Higgs boson with 5,154 authors. This kind of research often involves very large teams spanning multiple institutions. Typically papers published as a result of a collaboration are credited to all members of the team.