My daughter is 14. I let her get out since at a reputable body piercer because her friends bought piercing kits and all did their own and their friends septums and other facial piercings and all ended up with infections.
She let her friend pierce her smiley and that ended up infected. I decided if she's going to have it done by a friend under unsanitary conditions, I'd rather it be sterile and professionally done

Tell your child they will look like a bull. What school or workplace allows these piercings ? Does your child have or want a job? They look hideous in most workplaces

Are septum piercings really seen as that extreme these days though? Plus they can just tuck it away/flip it up when needing to hide it, if they get the right type of ring.

Not a chance. If they were over 18 I guess I wouldn't be able to stop them but I would strongly discourage it.

Is she at school ?

Not a chance. I’m not a snob but I’d draw the line at that. I’ve never seen a nice looking one, hideous.

I wouldn't pay for them to get it done but at 16 I would let them get it done.

If they were 16 maybe any younger is a big no for me.