you end up paying more the more money you have.

No, you pay the more you spend. This incentivizes hoarding wealth in investments.

Flat taxes are regressive. The poor pay a much larger percentage of their disposable income because necessities are a larger percentage of their income.

If someone makes $1k a month and it costs $1k a month to live, how is it fair that we charge them the same amount of tax as someone who makes $2k and spends $1k to live? We're forcing that first person to suffer so the second person can hoard.