Americans on the whole don't trust their government quite a lot. If the government just said "you owe X in tax this year", nearly everyone's knee jerk reaction would be that the government is overestimating and cheating them.
On the other hand, you can pay a flat fee to let a third party fight the government on your behalf. That's something that many Americans like the sound of.
I think the real problem is that the tax system is complicated, and turbo tax does a good job of making it feel even more complicated than it is. You can fill out your own 1040EZ, if you even know what that is, but people have this sense that the tax system is full of loopholes and they want to exploit that.