So you pay everyone the same benefit ( your tax-free allowance is basically benefits) and you make a huge saving by not having all the admin and economic incentive problems.
What about people who need extra help, do they still get more for disability, do people who need nursing care get it or does it all come out of their 15k year?
It's the same argument with flat tax. If we all paid a flat rate with no allowances, bands and loopholes you would raise the same amount paying 13% as we do now with 20%/40%. Except that assumes the billionaires would pay their 13%, which they wouldn't