It's really a question of political will.
Just think about the amount of resources the US spends on the "war on terror" or the "war on drugs" compared to the "war on tax evasion."
If the US gov wanted to reform the tax code and enforce everyone paying their fair share, they most certainly could.
The real issue, in my opinion, is that certain people have disproportionate influence in the legislative and rulemaking process, alas, we have the system we have.