Since you tagged this as serious… Is the plumbing in a chase? That would probably be a better route.
I could probably convince my wife we don’t need the spare bathroom upstairs so it’s not like the toilet will be used much or at least restrict it to non solids use to not cause issues.
Aside from probably not conforming to code, this should be a tough sell. The function of a toilet is straight forward and doesn’t involve restrictions due to communication cabling.
Have you considered running a second router as an AP or moving your networking gear to the main level? Either are probably less involving.
It depends. If it’s something I know I’ll use, especially a consumable, I’ll do it.