It isn't just that its meaning is bad. It is a word.
An actual word.
An actual word with a bad meaning. People use those in sentences. "
My mother-in-law is the bane of my existence."
It would be like naming someone Poison, Venom, Contagion or Contamination. I got all those out of a thesaurus.
Imagine your little Bane (your little poison?) sitting in class during the vocabulary lesson. Teasing potential? Yikes.
Don't. Please, just don't.