"This article ignores the 15.3% payroll tax that is split into two halves, each supposedly paid by the employer and employee."
You get a benefit for those taxes,  Income taxes fund the general costs of running the federal government: Defense, welfare, education, etc..  In fact, income taxes subsidize about half of Medicare's cost! So, don't whine about those taxes; you get a benefit!

I hate to break this to you, but your math is off. You say 54% of all personal income isn't subject to Payroll taxes, but's that's about 70% over what the the numbers show. 

$1.12 trillion divided by 0.153= $7,29 Trillion in income affected by payroll taxes*
In 2014, those taxes were $1.023 Trillion, with $6.7 Trillion affected by payroll taxes.*
Personal income (Total AGI) for 2014 was $9.77 Trillion in 2014 (the most recent year that IRS figures are available)

So, about $3 Trillion, or 31.5% wasn't subject to these taxes.
* Remember that SS tax stops; medicare tax keeps going. It's not all 15.3%