so, the argument would be to first make taxes more painful. the best would be to remove auto withholding. if the average $50k a year family had to write a check for $3k to the government every 3 mouths they'd likely push much harder for lower taxes. less taxes means less money for government which would seem to mean smaller government. once the taxes are low and government is small you can simplify the tax code.
I'm not saying I agree with that or that I could ever actually happen but I don't see a flaw in the logic and why their own description of their mission can both say they are for simpler taxes and also be against the kind of simpler the linked article is about