I don't see such a huge distinction between people and companies as you do. Companies are just groups of people working together. They aren't totally alien things.
Governments always claim that their tax is "fair", that doesn't mean anything. We have to evaluate fairness ourselves. In this case, what does "fair" mean? People tolerate taxation because they get something back from it. That's it - that's the only reason. It's not because politicians or governments have some natural right to exist, it's because the benefits outweigh the costs (again, in theory, ignoring that no government is even close to perfectly representative).
But what benefits do companies get from the tax they pay? The answer is, very few and nothing on the scale as what people get. Companies don't use roads or schools or hospitals, their employees use those and they already pay tax. Companies can use the courts, but they usually have to pay for that at the point of use, they don't qualify for legal aid or anything like that. They can also benefit from things like copyrights or patents, except these days at least in the tech sector patents seem more of a cost than a benefit. I'd happily opt my company out of that "benefit" if I could. They certainly are not immortal, companies go bust all the time.
Meanwhile, people that can't afford to play the game and make deals with Luxembourg can easily lose out badly in your so-called fair world. A few people form a company and start selling some products. 20% of the sale price goes to the government where the customer was based. But then, in the absence of double taxation treaties, the government where the company is based (if there is a single such place) would take another 20%. Then when the company actually pays the people who did the work, those governments might take another 20-40%.
0.8 * 0.8 * 0.7 (let's say 30% personal income tax) == 0.448, in other words you ended up losing most of the money you earned just to corporation and personal income tax. That's before including things like employment taxes, taxes on property and so on.
This provides a powerful incentive to simply not sell to other countries at all, and this makes everyone poorer. Which is why there are double taxation treaties. But once you have those, you have to accept that other countries will have different opinions about tax and different needs, and trying to slice up the cake will inevitably result in big fights and compromises.