I guess tax incentives feel strange because it feels a bit like a thing the government needs to do because of bad behaviors.

As you say, the situation would be 100% identical if the government was receiving directly the tax and then buying these things directly. So why don't they do that? Because people with money will find ways to dodge taxes anyway. Tax incentives is basically admitting that people with money are selfish and cheaters, and that we need to "play their game" to achieve what they should normally and ethically do if they were not detrimental to society.

Interestingly enough, if the person would have paid their taxes normally and that this money would have been used for a government project, then the probability of success would have been higher (I know some government projects are really mismanaged, but so was this one anyway), because the government would have been in better position to 1) get experts opinions/supports, 2) understand the rules and regulations, 3) synchronize different projects for a better complementarity.

I don’t think it’s because anyone has resigned themselves to thinking all rich people are cheaters who will win. I think we use tax incentives in the US primarily because of two beliefs - the first that the private market is often more efficient than public purchasing (which has a pretty poor showing from this article, as you point out!), and the other is that people can choose how to contribute some of their obligations back to society from the set of taxable deductions. We want to softly encourage some behaviors and discourage others, and adjusting taxes work well as a lower risk lower force way to do that.