Are there any legitimate uses for a shell corporation?
Every time I’ve heard them mentioned they’re always used to conceal something (usually money, but also just ownership, control, and/or material). Even wikipedia’s example of legal use is for the purpose of hiding your supplier and buyer from each other.
Specifically what it’s for - it is a name that runs a particular business, to insulate the real participants from exposure.
It may be to kep their names out of the news, to hide the names of the people involved (publicity), or to limit liability. (ShellCo built this bridge, so you can only sue them, not MegaEngineering Inc. ) Sometimes it’s a way of setting up a partnership between two groups and limit their mix and liability. A large corporation may think if they approach a person, say to buy real estate or mineral rihts - as soon as the other side knows “Hey, it’s MegaCorp, they can afford an extra million” the price will go up.
(IIRC when filming the third Star Wars movie in the redwood forest, the production company used a different name; on the theory “third megablockbuster movie?” the local catering, transport, hotels etc. would suddenly double in price. )
Could you be more clear about what you mean by legitimate? Maybe I misunderstood your question, but you seem to be accusing shell companies of not being “legitimate” because the exist for the benefit of those who form them, as opposed to existing for the greater good. If so, the answer to your question is no. However, under that definition, you could argue that any for profit entity does not serve a legitimate purpose.
What makes a company a “shell” company is that exists for the sole purpose of owning other companies. If they do actual things as well as own other companies, then they aren’t a shell company.
Most shell companies do not exist for the purpose of fraud. They exist because companies buy and sell other companies but often keep the existing structure of the company they just bought intact.
“Holding company” and “Shell company” are close to the same thing. Shell companies tend to own the entire sub-entity and holding companies may not. But when something nefarious is going on or suspected of going on, then the situation is always (AFAIK) referred to as a shell company. I think this gives “shell company” a pejorative sense that “holding company” does not have.
This has changed a bit recently as the phrase “bank holding company” has acquired a bit of a pejorative to it as well.
OldGuy stole exactly what I was going to say.
I do want to add that there’s nothing inherently wrong with wanting to conceal information. Confidentiality and privacy are important to companies just as they are to people. Most of the people on this forum are posting using fictional names to protect our identities from showing up in Google searches and the like. This doesn’t mean that we’re here for some nefarious purpose or being dishonest in any way. When an author writes under a pseudonym, they’re just trying to protect their privacy. It’s a perfectly legitimate practice, even if it could be used for illegitimate purposes.
It’s been my impression that the notion of a “holding company” has been around for quite a while, and has long had a perjorative sense, suggesting the parent company is concealing the fact that it is a big monopoly. I believe this connotation goes back to the days of the “Robber Barons” of the late 19th century.
Oh yes it does! 
By legitimate I mean not for the purpose of avoiding taxes, business laws, or liability. And not for gaming the market (like the example of concealing your supplier and customer from each other so you don’t risk them deciding your added value isn’t worth the added cost).
MD2000’s example of using a holding company to avoid price padding or extortion (as in the Star Wars example) is a good example of what I’d consider legitimate. A defense against an unfair tactic by others.
The Star Wars example reminded me that the Walt Disney company created a bunch of holding companies to buy swamp land when it was planning Disney World to avoid speculators demanding insane prices for a chunk of land that’d be basically worthless if it weren’t necessary for Disney’s plans (and worthless to anybody aside from Disney or other speculators).
Some negative examples of holding companies: anything related to the Prenda Law crew, Google (as well as Apple, Microsoft, and every other major corporation)'s foreign companies used to avoid taxes, and the three-letter companies run by patent trolls to conceal who owns what (the folks claiming a patent for scanning a document to email).