We don't need _more_ accounts, just simplify the ones we have and consolidate.
One unfairness is people who have spiky incomes, like a guy who repeatedly builds companies & sells them off, 4 years on ramen & 1 big payoff -- it does seem unfair to put him in the tax bracket of those with 5 times his average income. I have an idea many countries would let him smooth this out already, but don't know the details.
If you were worried about say, frugal people with large amounts of generational wealth, you can also pair this with a big fat estate tax.
Example: 12% tax on a Bentley or Toyota, Yacht or toy boat, wealth advisor service or lottery ticket
In this case, the last decade of monetary policy has been about pushing people to find passive savings unattractive. Their dreams of generational wealth from merely having a savings account totally wrecked because their life span cannot withstand the paultry compounding interest at a fraction of a percent.
Therefore creating incentives like you have imagined would further be at odds with the goal of keeping the money supply circulating, instead of parked in passive accounts.
The point is to keep everyone desperate for returns and using their entire mind share to find the best returns. Amongst the winners and failures you have individuals throwing their money across asset classes and the entire planet, which allows for easy accounting of the money supply and high velocity.
You could argue that people with higher incomes would pay a smaller proportion of their income as taxes, but this is beside the point--the only part of your income you can actually use is whatever you don't save or invest, and though you can just keep your savings and investments compounding indefinitely, you have absolutely no incentive to do so unless you are planning or anticipating for some future point in time where you or your heir withdraws and spends some of that money, which is exactly the point when that (typically much larger) sum turns back into taxable income.