To answer this question, I would like to use an analogy.
Imagine a kingdom with a good king, he was fair, just, and always made the best decisions for his kingdom and its residents.
Now, imagine a kingdom ruled by an evil tyrant, who terrorized the country side, with slavish demands, and lavish desires that brought his country to ruin.
The point I would like to make is this, the idea of a 'king' is not good or bad. The same thing with the idea of Nationalization (a nation or its people owning something, like a king) and the idea of Corporate takeover (a private corporation owning something, again, like a king). Which is better? Well it depends on the corporation and the nation, right?
Ok, how does this relate to LIG? Well, in LIG the proposal is that a country's (underline) resource will be managed by the country (underline) through a public corporation that is owned by the people. Im not familiar with what is happening in Denmark, but from what I understand the fear is that because it is a corporation that is not Danish, what fidelity does the corporation have to not abuse the Danish people. In reality, it could even be that Goldman Sachs will help the Danish people. Or not. It really depends on how they do. I would say the same for any corporation or business. I can't say anything definitive on this subject, because it is just speculating on the future. But your question does bring up some interesting concerns for managing resources with a LIG installed, so I will flesh that out, because it seems interesting, fun, and something important to do as well.
So LIG depends on managing a country's natural resources. It could be oil or gold for example (or energy as Anna's question demonstrate). I'm by far not an expert in the process of nationalization, so I will speak and speculate with what I know the best I can. So when a country has implemented LIG, they need a company and people to actually managed the resource. What would this include, well if its gold, it requires mining. Oil, you need to pump it out. The more efficient and effective a company is, the more profit they will turn out, because they sell more of the resource, while incurring less costs. If a company is poorly managed, or if the equipment is outdated or poorly handled, well, that would mean less profits, right? What's interesting is that (this is just my view point) a whole entire country will be essentially watching these companies managing their resource. So you would expect that they will be on top of the employees, and perhaps, I could imagine, the employees would have a sense of national pride, because they understand where the profits of the company go to. Imagine this, you work at the plant that processes oil, in a society that has implemented LIG. Well you tell someone, outside of work, what you do for a living, they would smile to you, and say thanks, because you are providing a great service. I would think too that, on top of that, the people would provide a nice wage to the employees of the plant. Because who decides the wages of the employees? The people do. Or at least they could. With the power of the internet, it would be easy to see how a company is doing, all they have to do is post it online. And because it is a public company, with no competition within the country, they can be as transparent as possible or desired. So these are my speculations and imagination on such a future and the relationship between the people at the nationalized companies. I would think there would be a close an intimate bond. It would be cool to see it in real life though. Let's make it happen, haha!
As my final remarks, I observed how LIG combines the "corporate takeover" and the nationalization, in the sense that there will be a public corporation that manages natural resources that is owned by the people. To the extent of my knowledge, no one has tried this before. Venezuela had nationalized oil, but it was owned by the government, not owned in the people's name (which is odd because the government should be synonymous with the people, which reveals the current separation existing between 'government' and 'people'). The same is happening in China too, I believe. A way I like to describe china's economy and political system is this, China is a like giant corporation called China that works on the internal markets as a capitalist. Comparing this to what LIG proposes, it is certainly dissimilar.