> There are caps to those tax advantaged savings accounts.

Caps that are set to the amounts where people start having enough money to hire a tax accountant and thereby use the various other ways of deferring income tax on money you're not immediately spending.

> You're still designing a system where the highest effective tax rates are paid by the lowest income people and the lowest effective tax rates are paid by the highest income people.

The status quo is even worse: They not only defer income tax on the money they're not spending, they defer it on money they are spending, by borrowing against the assets and spending the loan. Which a consumption tax would have them paying.

Meanwhile you can exempt necessities from a consumption tax to various degrees or issue a large fixed tax credit to everyone, which lowers the effective rate on ordinary people by as much as you like.