Tax the hero identity and the secret civilian identity separately
If Superman and Clark Kent claim to be two separate people, then they both need to pay their taxes. Any income needs to be reported by both people and they both need need to pay the tax. So any income of Superman/Kent is taxed twice.
This, of course, also hits those villains who also have secret identities while it spares heroes like Jessica Jones who operate under their real name. But these are rather the exceptions than the norm.
Tax psychotherapy
Many superheroes have to constantly deal with their personal demons. Childhood traumas, deaths of loved ones, fear of being inadequate, awful work/life balance, PTSD from particularly nasty villains, etc... Few superpowerded individuals do not fulfill at least one DSM-5 diagnosis. This should make psychological health care for superpowered individuals an important industry.
Many supervillains in fact did become villains because they did not receive proper therapy for their personal problems and subsequently turned their self-hate into aggression. So making psychotherapy unaffordable will not just increase the costs of living of superheroes, it will also turn more superpowered individuals into villains.