To anyone who does not believe getting foreign investments is a very important priority for Argentina, then we can just agree to disagree and you don't have to read the rest of this post. Foreign investment includes getting loans from organizations such as the IMF, the World Bank, and for foreign institutional investors to buy Argentinian bonds (especially new bonds in the future). It also includes foreign companies starting or expanding businesses in Argentina.
Multiple people have noted that others are using Milei for their PR or as a tool. I agree 100%, of course they are. That's how the world works. Countries use each other, people use each other. When influential people from other countries use Milei for their PR or political agenda, the name Argentina is talked about. The name Argentina and the business friendly changes being made are mentioned in the media coverage. Those allies also have influence in the IMF and the World Bank and would be more willing to support Argentina's interests in return. Of course there will be those who would like Milei to fail, but if they actively go against Argentina, that would be picking a fight with Milei the mad man. They have to ask themselves whether that's worth it. I think people are starting to realize it's not worth it because Milei will point a big spotlight on their weaknesses.
People like Musk and other billionaires probably want Milei to help them cut red tape and get some tax incentives if they invest in Argentina. Milei critics will no doubt complain he gives too much, no matter what the terms are, but the fact that they are even considering Argentina is an achievement in itself. At the beginning, you have to give investors some extra profits to offset the extra risk they are taking with you. You can renegotiate in the future when you have proven yourself. If you disagree with this, then tell us how you would like to spend all the tax credit that Argentina won't be giving away to the billionaires. [That's sarcasm in case you didn't get it because you can't spend the tax revenue on 25% of ZERO.]
For those who ask how many trips are too many, what do you think should be the right amount of advertising and marketing budget for Argentina to promote foreign investments and tourism, and how should those budgets be spent? How would their effectiveness compare to that of what Milei has been doing? Regardless of what your answers are, some of us are not going to agree with you. Milei wants to do it his way.
People say what Milei is doing, he is doing it for himself, for self promotion. Surely there is no better promotion for Milei than for Argentina to succeed under his reforms and leadership. So Milei's interests and that of Argentina are aligned. Milei being more famous means Argentina becomes more well known. As noted in the OP, Argentina can make all the changes in the world and it won't help if no one knows about it and the business community is not talking about it. So getting the name Argentina out there is a complementary effort.
Other also mentioned foreign critics of Milei. Well, he would probably also say again: "I don't care what they say about me as long as they spell the name of the country Argentina right."