From what I can tell, the system in the US is significantly more complicated for individuals (mortgage interest deductions, 43 different state income taxes, “alternative minimum tax,” gift tax, estate tax...)
As someone who has to file both, I found that the federal taxes to be comparable, perhaps I'd even say the Australian was more complex. The games played with real estate can be rather complex. But what I also saw was software doing most of the number crunching for me, and even fetching the numbers from my various employers and assets.
But your point about the state income tax is well taken, this does make it a much harder problem here than in Australia.
To be fair: Filing your taxes in the US is free. No one is going to force you to pay someone to do them for you, which is what TurboTax and the like are doing, usually through software.
If you don't understand the tax forms, though, or can't figure out the codes, you are stuck paying someone. The IRS won't give definitive answers if you call them.
This does not exist in the US the highest levels of government have no incentive to provide it.