It would work for a few years. Then more laws pass, court cases get decided, and the tax code would get more complicated. Now even TurboTax is a pain to use, and (as it ends up) the bureaucrats in charge of improving it are just as incapable as the ones rolling out healthcare.gov and similar disasters.
And then to deal with that, a new company emerges with a service that makes even TurboTax easy to use!
The idea that bureaucrats would competently manage it this time is difficult to believe.
From there, we'd just shut down or deprecate the original TurboTax service, and launch our rebranded fork as a free government-provided service like healthcare.gov (could call it taxes.gov). That would work as a short-term solution to make taxes easier for everyone, and it would remove lobbyist pressure against implementing long-term improvements like simplifying the tax code and automating everyone's taxes by default.