No, absolutely not. This would destroy morale for any up-and-coming entrepreneur/business leaders, causing them not to reach their full potential and not work as hard. Even though the American Dream has it's flaws, it inspires the populace to work their hardest, as this would evaporate. As a result, our society wouldn't be as successful as we could be.
How many entrepreneurs are there who would pass up the chance to earn $999 million because they could not stack another few hundred million on top of it? Since when has "being a literal billionaire" been synonymous with the American dream?
More it would stop companies from growing too large or those at $999 million would sell shares thus losing influence and control of company to stay under that. If company is worth $10 billion and you have 9% of shares, that will be a strong incentive to other reduce shareholding or not grow it further to avoid getting hit by tax.