The answer is in the question.
You said: They're descriptions of fictitious people designed to represent the common traits and attributes of a broader audience demographic.
Traits and attributes. Plural. They are made up combinations of several traits and attributes. Most people might have one or two, maybe even none. You might well spend a while finding the perfect real person who could represent a persona that you might otherwise come up with. Besides you still have to come up with personas to get to this stage.
Then you'll find they don't know what you think they know - or they know too much.
Don't get me wrong - nothing wrong with real users, but no need to get obsessive about finding users that could be personas. Just get a selection of real users - you can learn a lot from most users - they don't have to be the dream team.
Hopefully, you'll find personas are available 24/7, don't eat, don't sleep, don't get bored and don't need paying.
Move onto testing with real people when you think you've got enough content to make the feedback useful, but design/test/iterate with a representative selection of personas in mind, not for Dave in accounts.
EDIT: Added the following as examples of personas where the real person is going to be very hard to find:
Depending on how big the project, how long it's lasting, how much stakeholders need to be persuaded etc etc, then you might want to create quite detailed personas:
In A Project Guide to UX Design by Ross Unger and Carolyn Chandler (website: http://projectuxd.com/) they give some examples of advanced personas. You can find these on the website ( http://projectuxd.com/?page_id=5 ) under Chapter 7.
You can also Look inside the book at http://www.amazon.co.uk/Project-Guide-Design-Experience-Designers/dp/0321607376 and then Search inside this book for Advanced Personas and going to the second result (using the tab at right of 'page')
Now these personas are intended to be detailed and for good reason. As a developer or designer you should get to know these people; to understand them; get their needs, desires, influences, goals, doubts, etc. The more detail, the more real they seem. They should live on your wall; in your head, affecting your design. You should feel empathy with them.
BUT - These are not real people - they represent a type of person in your target audience but they are totally fictitious, maybe made up from hundreds of collected details, all accumulated through researching your audience carefully. To research your audience on a broad scale and then pick a real person as your persona, is like arranging a whole bunch of focus groups and then listening only to the one person that shouted the loudest.
Where are you going to find a single person that encapsulates all the information from one of these advanced personas.