Cooperation between parties with differing goals and management styles results in design (and subsequent dismissal) by committee, whereas competition unhindered by interference from the motivated parties results in landing humans on the Moon.

Yes, if everyone were altruistically motivated to get humans to Mars, we would all contribute our dollars and work together to make it happen.

But in the real world, a lot of people who don't care beans about Mars can still be motivated to invest in the effort by the prospect of investment gains. And those gains require for-profit competition.