Just a comment first: they're all "real people", the difference between both scenarios is one of them is staged and with obvious models, while the other is just casual. If you use the same "beautiful" people in no staged, casual scenarios, they will turn "real".
The above is because this difference is fundamental in the answer, which has several different parts:
Stock photos are cheap if you have to hire a professional photographer. Of course, as you mention, you could take the photos yourself, making for more realistic, in the wild photos. But...
...problem is everybody wants to be beautiful and flawless. Many times, if you go to an office or work place and tell them "let's take a picture" they will feel awkward and uncomfortable. And it shows on the photo. Some people will even refuse to pose. And many company owners and managers will think "I don't want to show my real life flawed employees, I want to show how beautiful we are!". This is most common than you think, as a matter of fact is the vast majority (hence Stock Photography sites)
Broad Subjects for Design
With stock photos, you can find literally thousands of options for your designs, in a wide variety of subjects. No matter how good of an amateur photographer you are, it's almost impossible to compete with the variety of options at the same cost. Think about this: not all sites wants/needs to show the "behind the curtains". As a matter of fact, most of them don't need it at all, but they need the mood. Which leads to another thing: the creation of mood boards: when you create a mood board, you will be almost certainly use stock photos or Google images. This will influence the final design and more often than not you'll end using an image you have seen when building your mood board
Obviously, you have the "laziness factor": designer is left with "make it pretty" and companies won't ever provide any material at all, let alone personal pictures (so far, unless I get almost to the verge of annoying the client, I have NEVER got a personal picture at first request. NEVER IN 19 YEARS!). As you may imagine, stock photos are the salvation here
History and Cultural Background
Finally, Stock Photo services are (and have been) used by printed media and advertising companies. First stock photo service was created in the 1920s decade, and based on contemporary history and cultural development, you can't say it was a wrong idea!
The above is to explain WHY STOCK PHOTO SITES DO THIS. Whether to use "real" or "fake" photos will entirely depend on your site, mood and approach.
People is used to "fake", embraces it, do it themselves, many people try to have cosmetic surgeries or at least photoshop their pictures.
If you try to sell a perfume with your neighbor and your digital camera, no matter how pretty she is, the ad won't work. Think about this: companies aren't stupid and they don't spend billions in "fakeness" just for hobby, this is an aspirational principle! Take a look at McCann's article Truth abut Beauty for a more detailed explanation.
And of course, if you want to do a site about a software company or gardeners or whatever, the "real people" approach will work better, because you're deviating from aspirational to productivity models
If you need to get "real" stock photos, there are lots of sites where you can do it. Even better, for free. As an example, check Morgue Files and Library of Congress Photo Catalog