The basic issue is caste defined as the absence of personal responsibility and freedom from consequences.

The free market pirates invented an interesting new spin on this pseudo-aristocracy, but given time they'll think of another one.

Income taxation won't solve the problem because the issue is now international, and needs to be enforced consistently across the planet. If the rich don't want to pay exotic taxes they can always redomicile. Off-shoring would have to be eliminated, as would capital movement and speculation on foreign markets.

Estate taxes would possibly be more helpful. Kids have much less freedom of movement than adults do, and taxing inheritances and closing avoidance loopholes would catch the cash at the point where it can prevent the idle rich using their inheritances for political leverage - which seems to have beenb one of the root causes of the current situation.