These have probably existed forever – organizations that claim to do one thing, but were set up by other organizations to do their work for them – in secret. These were common in palace intrigues the world over. Wikipedia has an excellent discussion of these.
In our time, one of the vital activities of any businessman or politician – is to figure out who is who – relationships that are constantly changing. They all know things are not as they seem.
Shell companies were part of Big Business, that developed late in the 19th Century, and early in the 20th. Industrialists (also known as Robber Barons) formed plenty of these – but it wasn’t too hard to figure out who was behind them – the guy who ended up with all the money.
With the coming of the Computer, and its Internet – Shell Companies became much harder to detect. Bin Laden used plenty of them – and his network spread everywhere.
People wanted the bad guys to be exposed – but not them, because they are often part of some scam or other themselves.
But separating the two can be difficult.