The problem is that the system requires constant maintenance every time some tax law changes in any state, and great maintenance is something that only the most well funded OSS projects get. And you need participation from lawyers and accountants, not just software developers.
As the article notes, there are already free solutions for people with basic income situations (W-2, some bank interest, no stock sales) making under $66k. Personally, I don't mind paying $100 to turbotax for the peace of mind of knowing that at the very least, they have a staff of tax experts looking over the details of their filing process.
Now, if the IRS came along with an official app that showed me what information they already had and I just needed to make some small adjustments from there (assuming my tax situation isn't complicated), then yeah, I'd use that. And it's a bit crazy that we don't have that. But unlike many countries, we are taxed at both the federal and state levels, which makes the process much more complicated. And to complicate things further, the two interact: I can deduct some of my state taxes from my federal taxes (though less than before). And don't even get me started with the complications of a move from state to state.
EDIT: thinking about this a bit more. What really annoys me about the current system isn't necessarily that I pay to file my taxes. It's that it's so easy to miss things. Maybe i have a bank account that earned $12 in interest and I earned $20 from money that I put into lendingclub.com two years ago. It's annoying that the government has this information, but on the other hand, it's very easy for me to not see (or forget about) the email/snail-mail that I got about this income and then forget to declare it on my taxes. Yes, I know that the IRS isn't sending me to jail for forgetting to pay $5 in taxes, but in general, the process would be much less stressful if I had some kind of centralized reminder of all the income I made.