Indeed, lots of other figure skating elements are potentially injurious too. Ice dancers can also get concussions or knee/back injuries from lifts, but nobody is debating dance lift rules.There are plenty of ladies (and men of course) who got injured or even had to stop their career while never training quads. Even ice dancers.
Also pairs obviously has high trauma potential, e.g. being dropped from a lift, landing wrong from a throw, or even freak accidents like side-by-side pair spin collisions (Berezhnaya or Dube). These skills can't be omitted, they just have to be trained carefully to reduce risk.
About ladies, Biellmanns can cause or aggravate back injuries particularly in less flexible individuals. But they are generally seen as a 'ladylike' move, so maybe that's why they get less scrutiny than quads? (that and the fact it's possible to get L4 without them, albeit with difficulty)