Beside that and not speaking about darks. What other solutions may people have to setup a anonymous company you think?
I think that we may be reaching a point where the question needs to be rephrased, so we could drill down deeper.
Having said that I think the purpose of why we need that anonymous company may have direct impact on suitable solutions.
What I mean by this is there's a big difference in the whole approach if we need this anonymous company to be able to run an anonymous business (and pay zero tax) and it's different when we need a company that is not in our name to be able to generate costs in connected companies. (there may be more reasons, but I can only talk about those two...)
I think that the market of agents and companies, agencies that are able to form LTD/LLC company in UK/US is enormous and in UK like in US no one is really checking anything. To put it simply this is the place that should be exploited. I've managed to form and abandon multiple companies that have served their short lives and no one really cares.
To change this situation the law would have to change and remove a possibility of forming a company on behalf of a third party, which would kill a lot of businesses. Then those businesses they check what they need to check but not more as that would go against their best interest and would eventually have negative impact on their market.
Depending on the actual reason behind the anonymous company, it's possible that a suitable option may be registering a company in a reputable state (with complete FAKE data). Assuming this is for costs generation, analysing and emulating Winglio process would be a safe option ( I strongly advise getting a dark account in there to explore how it works inside out and then it's totally possible develop same or similar process.
Naturally payments would be a challenge so again depending why the company is needed, I would not be trying to get any EMI account, would just arrange paying invoices by credit card instead of wires and actually at the time of payment the money can be converted into crypto, and then God only knows what happens next...
This is not Mentor Group so don't want to jump in exact details but this is more than enough, I think.
Alternatively, if you you need an anonymous company to run a business long terms and to actually run it I don't think there's a better option than using darks and getting a proposer setup for it. However I think that it's much more challenging to keep a number dark companies long terms (several years+). This is because there's a bit of reporting everywhere, no matter the jurisdiction (I'm personally only interested in US/UK) and at some point this becomes too time consuming and / or requires some help from the third parties and the more required from those third parties the less secure and less anonymous the setup. When you reach that level if things come out it may be life changing dangerous in terms of consequences. First the law and being a criminal, but equally dangerous can be being exposed to those third parties as an extortion might be a good option for them and in many cases natural thing to do. And this is actually something I know something about, so the less anyone knows, the better.
All in all I think that understanding of the process and tweaking the process for particular purpose is far more important than the particular steps. In the same process it is crucial to understand where and when a human factor comes into play as this is the only place where the outcome is not boolean.