I think 99% is an overkill. If you assume 7% ROI and 2% inflation then a 70% top marginal bracket (combined with unifying capital gains and income) would make it very hard to maintain wealth.
To get rid of these high levels of inequality we don't need to make it impossible to be rich, just make it very hard to be rich and let nature take its course.
Note that in my lifetime the top marginal tax bracket has been over 70% so it's not even that radical of a change.
At 2% inflation, it's not possible to maintain $100M of wealth without also having $2M in annual income. If every dollar over $1M in income were taxed at 70%, then you would need over $4M in annual income, plus more than twice your annual expenditures to maintain that level of wealth.
4% rent on $100M in assets is probably sustainable over a long time, so if you live frugally, you could likely self-sustain that level of wealth.
If you have $1B in assets and make a 7% return (which is my conservative estimate of the maximum long-term rent you could extract on a large fortune) then that's $70M return in income, essentially all of which is taxed at the 70% rate, leaving $21M remaining, $20M of which is "lost" due to inflation.
This means that if you have a billion dollars and want to live just off of rents, you would need to both invest prudently, and live on expenses of no more than $1M per year. Mess up either and you are on track to leave the billionaire's club.
In addition, consider an heir who gets a high-paying professional job with a rags-to-riches one. The one with no wealth isn't having unearned income to pad their tax bracket, so the marginal pay they get for working is much higher than the heir who is also collecting investment income, thus allowing them to grow their wealth faster if they have an identical savings rate.
The US right now has an income tax scheme that is regressive for wealth because wealthy people have a greater fraction of their income in the form of long-term capital gains. GP suggested making it extremely progressive vs wealth, and I'm merely pointing out that a properly implemented wealth-blind income tax will work out to be progressive vs wealth due to inflation.
To get rid of these high levels of inequality we don't need to make it impossible to be rich, just make it very hard to be rich and let nature take its course.
Note that in my lifetime the top marginal tax bracket has been over 70% so it's not even that radical of a change.