Entrepreneurs "have business to do" as Mark puts it because they stand to make some money from their efforts. The less money they stand to make, the less incentive. period.
Also, you state the following as if its fact:
"what capital gains taxes really do is favor the ultra-wealthy who live off of their investments, rather than those generating wealth directly"
No. In order for the ultra-rich person in your example to have accumulated $5M, he EARNED $6,750,000 and paid the government $1,750,000. So, by paying tax on his investment income, he's paying tax twice on the same money. That simple error aside, you're also missing the point that capital gains tax discourages investing in companies! Which has an impact on a company's cost of capital which has an impact on the price of goods and services which has an impact on you.