1. Have real practical advantage over other people in their community 2. Have real practical power to shape their community
For #1 that's mostly the middle class, who want better schools for their children, and safe pleasant environments for their families. Actions that remove that incentive, make the middle class irrelevant. Very few people are willing to work 9+ hour days during the start of their career, just so they can have more toys, and not a larger house in a good neighborhood later in life.
For #2 that's mostly the elite. If they're denied influence via money, they'll simply go into politics or religion where we'll end up with a society shaped by lucky charismatic people, and not necessarily anyone who has any skill. At least we can say non-hereditary wealthy people are lucky, and skilled as opposed to just being lucky.
You'll certainly remove their clout over society but I think you also need to consider the significant downsides to this proposal. Maybe you would be better off finding ways to limit the power of rich people over society (eg political contribution laws) instead of trying to ban being rich?