It's not a terrible solution. Ideally a flat tax (which pretty much always means a lower rate than high earners pay) simplifies the tax system, and makes high earners less likely to evade taxes. However it doesn't change the fact that really high earners get a lot of their wealth from investments, so in the end they'll still pay a lower total 'rate'. The highest tax burden will still be paid by upper middle-class professionals who have a high salary but few investments.

If governments really want to collect taxes from the ultra-rich, a wealth tax is what is necessary. However that alone poses problems because 'wealth' is not always liquid - do you tax the old lady whose house has appreciated significantly but who doesn't have an income? Do you tax an entrepreneur whose firm is worth several million but hasn't actually realized any significant income?

Anyhow, just a few musings, but the summary is that taxes are hard. Too high and people evade them, too low and the government has a shortfall...