The main argument I heard against simplifying the tax code (and allowing automated free filing) is that it would eventually lead to a slow but steady increase in taxes. Another way of saying this is that: the "pain" of paying taxes makes people scrutinize the tax code and acts as a deterrent.
If you were to frame it in that context (and if that statement were indeed true), I am sure more people championing a simple tax code would stop doing so. I would rather pay $100 to Intuit's potentially unneeded service than $1000 as a tax increase.
I am not claiming that it is true - I don't have a way of testing this hypothesis - but it is something that is worth musing about. There are always unintended consequences.