Also there is plenty of business income that is not double taxed because it isn't run through a C Corp.
Then in regards to incentives. We already have interest rates to adjust the knobs of investment versus consumption. Capital gains is just a way to make the tax system less progressive.
However, once you earned enough money, beyond subsistence level, you have a choice - you can spend it all on consumption, or you can defer some of the consumption, or give up a part of it, as an investment, in hope that this would increase your consumption abilities in the future, or you ability to retire, etc. Modern economy would not work without investment - you need massive upfront spending to lift off something like Netflix of the ground, before it starts being profitable.
This investment is, ultimately, financed by people who chose investment over consumption (might be one very rich person, or tens of thousands of not so rich people giving their money to the bank, which in turn loans it to the entrepreneurs, or likely a mix of both). Ensuring this choice remains a viable and attractive one is something that the government would definitely have an incentive to support.
Moving onto more statistical approach, this one: https://www.fa-mag.com/news/most-millionaires-self-made--stu... says only 8% of millionaires inherited their wealth. For billionaires, according to this: https://www.entrepreneur.com/article/269593 18% got a jump-start (maybe parents were mere millionaires, but the child became a billionaire), and 62% are self-made. So inheritance effects exist, but maybe they are not that huge? At least, clearly, not a majority.
Of course, not everybody starts in the same place. But human behavior and motivations are similar, and thus you can reason about them despite the differences.
Also, realize that the government does promote both labor and investments, just through different means. Lowering taxes isn't going to affect how a fully employed individual produces labor; they are trading their time for money. Lowering taxes on investment will promote more investments, since the money for those investments have already been taxed, and since the trade of investments is money-now for money-later, taxes have a much more significant influence over the extent to which someone will invest in a business. Someone fully invested in other things (non-stock commodities, etc) might move some of their investments into businesses instead.
Of course, there's a political component of it too - taxes are always political, and are used to promote or suppress certain actions. I guess the government does want to promote long-term investment and thus defines lower tax rates for this activity.