Really not that simple as that.
You are incredibly knowledgeable and skilled in technology and
anonymity, but when it comes to business structures and reasons for setting them up, your answer is indeed lacking in objectivity and proof of concept.
These were mere examples and based on what you quoted sure I can agree from a linguistic perspective. I should have said:
"If you have a legal business
in most cases you do not need anonymous company. If you have restrictions based on laws or taxes are eating in your margins
the easiest/cleanest thing to do without getting involved in schenanigans is to -> relocate."
The forum is full of examples and proof of concepts. But let me more specific with some concrete ones.
Anything can be a but and an if, exception to the rule, exception to the law, exception to the law in practice and so on. Without a doubt you can have a legal business and want to make it anonymous for example just because it is illegal in country A does not make it illegal in country B. However once you connect it to your real world identity through for example other companies or structures, it is no longer 'anonymous' even if not under your name. An excellent case study for this if you do not believe me is all the bank fraud that is done through bank transfers. Take a look at the court documents of convicted fraudsters (for actual "proof of concept") how they easily trace everything because it is recorded. Many of these operations run through fake or mule accounts and then receive their profit in
cryptocurrency. Wonder why that is?
Why not setup 'anonymous' companies and tunnel it to there (and some other accounts maybe) and then to their personal bank accounts? Hint: dropping soap time regardless of how long your chain is. As I have mentioned it takes one determined investigator to uncover it. Because you are not uncovered due to lack of man power, funding or care (no one cares if you are a small operation in most cases), that does not mean 'they' do not know.
These are all semantics in the realm of laws, regulations and other bureaucracy. In reality, it either is anonymous setup using what is referred here as '
darks' or actors, which does not guarantee reliability, and that can serve as a 'gateway' to anonymizing your earnings, or the 'anonymous' part is only a word but not actuality. It highly depends on your threat model as well. If you are doing something which say is considered illegal in environmental aspect in country A, but legal in country B and you are trying to bridge to make the business work then your threat is most likely environmental agencies, some lawyers and some level of low-mid level law enforcement. If for example you were a someone doing bank transfer fraud as per my example then your threat model is entirely different where if you get big enough you can get the entire world against you (e.g Gameover Zeus crew). However to continue the same example the interesting part is once you push the system to its limits you quickly realize how 'anonymous' is simply a word, not an actuality in the traditional banking/companies system hence the use of mules and other 'sanctioned' methods while converting the end result in cryptocurrency.
How can it be useful for me for example to open anonymous company in Switzerland for example?
OP asked how can it be useful to have an anonymous company based on
crypto trading activities. The reality is with that specific activity he can not as it is still considered 'taboo' and brings extra watch. He can hide behind trusts, partnerships and all kinds of complex structures and he will achieve privacy (even possible on level of not appearing on UBOs) but not anonymity. Anonymous is when no one knows who you are. Privacy is when no one publicly knows who you are. If you setup your company and one lawyer firm has all of your documentation and know who you are - you are not anonymous, you have the cover of privacy. Not to mention lawyers and other key facilitators in 'potential' anonymous structures are common target for surveillance by intelligence services - it is very different from the movies.
My point was something else, it is not a dig at your industry or services. There is no real, true & total anonymous company unless you use it as a 'gateway' as some of the examples I have mentioned. It is a all traceable. You either set it up anonymously and have no control over it (specific example think you share access to company cryptocurrency wallets with second person...) with the benefits of say no liabilities or you setup a company through the privacy layer and are responsible based on the laws of the countries you have decided to use(/stack on top of each other) to get the specific protection and privacy features of it(/them).
To be completely accurate and detailed of exceptions as that was your criticism, yes you can setup an anonymous company here and there and get away with it. However, in specific to the West, disrupt the agenda and say there are only 2 genders and watch how all of these 'protections' will be gone in a second while bringing up all your past indiscretions (yes, democratized blackmail). Many examples of this. The old saying 'if they want to get you, they will find a way' is very true and if you believe fancy oxymorons like banking 'privacy' or corporation 'security' will truly protect you when they actually do come for you, reality will shift before your eyes.