I do agree that she has a lot of popular songs that do well in charts, but what is exactly her influence? I don't see anything that has changed after the happening of Billie Eilish in music or pop industry. Nobody tries to imitate her, expect 14 y.o. people on TikTok.
After Lady Gaga literally every other singer in the world was trying to be weird and out-weird each other in their outfits and music videos. Let us not pretend Katy Perry, Rihanna and Nicki all thought at the same time to wear wigs and go from trashy pop girls-next-door to who they are now. Billie is certainly a big pop star and she will remain such if she (read = her team and her brother) plays her cards right, but she is nowhere near an icon status.
If I were Lady Gaga, Madonna, Amy Winehouse, Whitney Houston, Janet Jackson, Katy Perry or even Taylor Swift, I would not appreciate being put in the same ranks as Billie Eilish. She hasn't penetrated yet the older generations enough to become iconic, all the other women are known worldwide throughout all ages. I am pretty sure in Eastern Europe, where I reside, the majority of people above 35 y.o. have no idea who Billie Eilish is.