Cheaper and covers more people...

Watching either the CNN or MSNBC debate Herman Cain said something about the free market making things cheaper and covering more people. I could look it up but then I'd be tempted to take on the specific example instead of the philosophy.
There is a fine line between me and (many/most)conservatives on this but it's an important line. I think that the free market CAN offer cheaper services that reach more people than a government program. But I do not believe that it always does. There are several reasons for this, including:

Incentive
Government programs and businesses have different incentives. A government program is created to serve the masses, who often have more votes than dollars. A business is created to make money. A business is obligated to make it's stock rise every month (greed is a legal obligation in a way). And serving more people is not always going to be the most effective way to make money.

Imagination
Sometimes the market solution just hasn't been thought of yet. I don't think it's impossible for a private business to do a better job than the post office. But I haven't seen anyone come up with the way to do it yet. What about FedEx or UPS? Let's just say apples and oranges for now.


Inertia
If a company is already making money serving a few people it is less likely to go out of it's way to change it's strategy to widen it's costumer base. FedEx and UPS are competing with each other on shipping boxes. They are so busy trying to come out on top over the other they might not even have the resources to invest in trying to figure out a way to send one or two pieces of paper for less than fifty cents a piece.

That's it for now but I'll be sure to expand on this as I come up with more. There may be an argument for why government shouldn't get involved with things like healthcare or delivering the mail. But for now I am focusing on whether or not the market is always the best solution for the most people. The answer is only if helping more people equates to more profit. And it raises another question. What do we do about all the people the market doesn't help?
The government didn't take on all these responsibilities on a lark. There was a vacuum.
Public Schools were created because the private schools weren't educating enough people. Obamacare was created because insurance won't/doesn't serve enough sick people. OSHA was created because it is sometimes cheaper for employers not to provide a safe work environment. And welfare was created because living expenses were not low enough for the under- and unemployed.