I have no argument with you, Major, and I don't know what company (if any) you represent; but I'd like to answer your questions and provide the perspective of those of us writers whose situation is just not accurately described by what may or may not be true "on average":
That's a wishful thinking. Freelance writers working on their own may on average expect up to $15-$20 per page.
That might be true "on average" but not for good, experienced, American and British freelance writers. I haven't written a single page for a penny less than $30 in at least 2 years and I believe Pheelyks hasn't written a page for less than $35 or $40. The other 2 good experienced writers I know charge the same. All of us also work for some of the same essay companies and that's one reason we've gradually shifted quite heavily to freelance work.
If you do, what are the main reasons?
The main reason is that many customers prefer the certainty of knowing that their work will always have the consistency of being written by the same person and at the same level instead of by whichever company writer chooses to take their order. They can (and do) ask for us by name at many companies, but if we decline it (and we often do), any other writer (of hundreds of writers with varying skill and experience levels) can take the order unless they specify that they prefer a refund if we're not available. If any freelance clients of mine ever need work outside all of our areas, I have referred them to companies that I know are legit and I've helped them phrase the description for company orders that help them get what they need.
Just because they use their own private email doesn't mean a student would have to pay 100% more to render their service.
From the customers' point of view, they probably don't care if they pay $30/pg (or more) to a company that only pays about half of that to the actual writer or the same $30/pg all to the person who's actually writing the paper. Whether it's a company or a freelance writer, customers are often (understandably) very apprehensive placing that first order, but once they get a good product from a freelancer, they might actually feel safer knowing that it's always going to be the same person writing every order. As many customer testimonials here illustrate, it's quite possible to get a good essay from a totally legitimate company one time and a much worse essay from the same company subsequently, simply because it was written by a different writer.
- There is no protection using an individual freelance writer.

I can't speak for any other writer outside of the small circle of 3 or 4 good, very experienced, honest American/British writers I know, but if one of us has an occasional emergency, we do the responsible thing by contacting one another for help. We also happen to be the top writers (of hundreds) at the essay companies that use all of us, so when it's a freelance-work emergency, at least (in our case) our emergency will be handled by an equally good writer. If the same thing happens with a company writer, the order either goes right back to the pool of hundreds of writers or the company contacts its best writers asking for help with it. As it happens, we're the same 4 writers (out of about 5 or 6) who our companies will approach first, asking whether we can complete an emergency and they'll offer us a bonus for doing it; but even with the bonus, it's still less than we (now) make from our freelance work.
Finally, no company I know ever "assigns" or "reassigns" an order like that to another writer to complete it because we have no obligation to take any order we don't choose. The most they can do is ask one of their best writer to help and then, if we all decline, they just repost the order for all writers to consider, and usually with a bonus to make it more attractive, hoping someone will take it. So, when it comes to emergency situations, the customer is usually in the exact same position whether it's a company or a freelancer, and in many cases, it actually involves some of the same writers in both cases.