Because of the complexity of tax regulations, I don't think coming up with a competing free/open-source/nonprofit tax preparation service is the right answer to this problem.
Let's consider the positions of all sides:
* The professional tax preparers are worried that they're going to lose business if the government assumes the bulk of the tax preparation work.
* We as taxpayers would prefer that the government pre-fills a return for us, since they already have the information, and lets us file the pre-filled form if we detect no errors. That saves us time and also lets us see what info the government has about our income.
* But we also recognize that it's in the government's interest to maximize the tax we pay, and (ideally) it's in the tax preparers' interest to minimize the tax we pay.
Given all that, if pre-filled returns are unlikely, for political reasons, then perhaps a step up from the current Free File program might work like this:
1) You go to a Free File partner.
2) You authorize the IRS to release all of your tax information to that partner, who pre-fills the forms.
3) The partner walks you through the pre-filled forms, so you can check for accuracy.
4) The partner then does its own checks to discover errors that you might not have picked up on.
5) The partner makes money by selling optional add-ons, such as audit protection services.
This would, at the very least, speed up the Free File process and let you see what info the IRS has. It also ensures (like it or not) that the partners keep getting business (or at least eyeballs to pitch extra services to), and it ensures that your interest in paying the least amount of tax possible is reasonably protected.