PM me if you want a reliable (=has 20 years experience with servers even for large operations or secured operations like banks) hosting owner for a gambling operation
I recall how he saved my neck, when I put on my website a parody of a anti-gambling finance minister in a country where the mafia= the government (ok, probably all countries are like that). The server was even in that country. And really came request to reveal my identity! Well, all good...
In normal corporate hosting no one really knows whether it is fully private or not. It is not actually just about anonymous payments, it is about full privacy, where the hosting must understand that they have to cooperate with authorities only to the point where law demands it. Hosting employees do not understand it and the larger the operation the less they understand it. For example when police comes and asks about info, they usually just try that. But in most countries no info has to be usually given to them. It has to be just most likely a court decision.
And here is the crucial question. If you want full privacy, will the hosting not cooperate with police where they do not have to? Will the hosting provide something like warrant canary? Will the hosting fight at court for the sake of privacy?
It is about the budget of course.
If you talk to God, you are praying; If God talks to you, you have schizophrenia.