These arguments use a simplified model where capital income occurs as the consequence of investing wage income. They don't address the modern reality that capital income replaces wage income, through accelerated depreciation, inheritance, carried interest, etc.
And yes, of course taxing capital is distorionary; but so is taxing labor, and exponentially so when capital income may be substituted for labor.
My personal view is that the pro-differential-taxation theory mostly argues for zero taxes on cap gains. But you're right that this ignores political and economic realities. In particular, I find the discussion about the difficulty of distinguishing between capital and wage income (the topic of Fred's blog post!) particularly compelling. So a compromise is in order: lower taxes on cap gains but not all the way to zero.
This is, not coincidentally, the status quo in the US and most other western/developed nations.
And yes, of course taxing capital is distorionary; but so is taxing labor, and exponentially so when capital income may be substituted for labor.