They absolutely are. Genres are merely vaguely-defined concepts. Pop music is the broadest umbrella under which music can be placed. By its own definition, a pop song is a song that has broad appeal to a wide audience. Only over the course of our lifetimes has pop music taken on an additional but secondary meaning as a more specific style of music. The meaning of "pop" and the songs that are "pop" do not create a mutual exclusivity.
No. The TERM "pop" originated from popular music, but the term was created for simple songs that follow current trends and attempt to appeal to the widest possible audience, deemphasize artistic qualities, and focus on production over performance - pretty much none of which applies to any of the songs I named.
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Fresh from my first justified ban. Ever!