I would tend to agree with you. But I feel I must present some counter arguments.
- Bugs Bunny is an icon really only in the U.S.A. He has little international relevance. He's actually banned in China because the CCP consider him a bad role model. Unlike say Mickey Mouse, who is recognized around the world.
- Bugs Bunny has never had prevalence in print media. TV and movies, sure. but not in books or strips. unlike say Snoopy, who started in print and moved on to TV and movies.
- Adults are more into Bugs Bunny merch than kids. For whatever reason, actual children don't really embrace Bugs Bunny as a toy. He's not cute enough in a child's eyes.