In stories, there is a tendency for the most interesting characters to be specialists, while generalists tend to be not as interesting. I'm talking about characters here, not mechanics or rules. I'm not talking systems here. I'm talking about how fictional characters get more interesting the most specialized they are.
This has to do with the nature of limits. The more specialized a character is, the more limits they have. Limits (sometimes we call these laws) make characters more interesting. They keep a character from bulldozing over obstacles. Good stories are about overcoming limits. Great stories are about characters admitting to these limits- maybe they overcome them, maybe they don't.
This has to do with how we humans as audiences empathize with the character- if they can overcome their limits, it satisfies a urge in us as well. When characters come to terms with their own limits- it can help us as humans learn to realize our own limits. This mythological cornerstone explains why characters with limits- flaws and complexities are more interesting to us.
Here's my main example for this: Harry Dresden, from the Dresden Files.
Harry is a Wizard and he's also a Private Investigator. Despite being a Wizard- Harry's human. He specializes at finding things, causing trouble and fire magic. Harry specializes as a Wizard and a Private Eye. Memorable moments in the series are when Harry meets his limitations- sometimes he gets confronted with them by his enemies. Key to Dresden is how he rarely backs down from his limits. He hits them, like a race car crash. Dresden isn't good at everything: if anything, his limits come up almost all the time.
Being a Wizard doesn't help: it makes Dresden unable to use technology at all. That alone makes stories with Dresden interesting- He can't use the internet to solve a question. He has to look for the answers himself.
How does this apply to RPGs then?
I write this to point out how, as a Game Master and a player, specialists tend to have more story potential than generalists do. Where a generalist has a tool for every job, the specialist has to think of a solution to a problem. They have to be creative in their problem solving.
Specializing means you have a spoon for most of your problems. Looking at it one way, you can only use a spoon to do one thing. But looking at it another way, a spoon can break through locks, torture people or kill a man. Its a matter of explaining the how, and how your specialty comes in.