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.

I think a big fraction (the majority) of people who hold the belief that private market is more efficient are also saying things like "you should not do X or the private companies will just go in another country where they don't impose X", with X being usually a thing beneficial for the community/society (collecting fair tax, protecting the employees, protecting the environment, redistributing the money towards basic infrastructure where people cannot afford them, making sure the market is fair, ...). Trying to avoid any of those X is usually morally questionable (and on top of that there is the fact that they will not hesitate to turn their back to the country that provided the environment were they were able to be successful).

So, a lot of these people who hold this belief are agreeing (not explicitly, they just know it's true but don't want to say it out loud) that rich people are doing what is better for them, not what is better for the society. Which is why people view negatively rich people who profit from government tax incentive.

I think you summarize my understanding on why using tax incentives are seen as a negative trait with the sentence

> We want to softly encourage some behaviors and discourage others

If you have to encourage behaviors that are good for the society and discourage behaviors that are bad for the society, it means that some people, without these incentives, will prefer to do the "bad" behaviors rather than the "good" behaviors. I understand that people will not like these people.

Again, tax incentives are totally useless if the rich people are people with normal moral who will naturally try to do the correct thing. The government, not you, is already choosing the domain where it applies tax incentives. So the argument that you don't want to give tax because you think you will do a better job at choosing the project than the government does not hold: if you are doing something where the government provides a tax incentive, you are doing something that the government wanted to be done. And the government is also more than happy to get good advice and support on such projects, but again, there, those generous rich people are not doing anything despite their nice posture. If indeed they don't trust the government to do "good things", it's funny that they don't do them themselves and instead jump on the first tax incentive opportunity. Posture is cheap, but when it comes to invest extra, without government help, for something that is "good", there is no one remaining from the group of the people who explains that a government collecting tax is not a good way to have nice things done.