There is definitely an argument for and against in using a Third...

There is definitely an argument for and against in using a Third Party to negotiate a sale of anything.
Granted too, some people may feel uncomfortable dealing with the vendor direct and prefer to be "anonymous" in their dealings to purchase.

But if the price is realistic, and a person likes and wants the place, is he going to walk away because it is a private sale? You have done your homework, you have a budget,you have already looked at some property and know roughly whether or not the asking price is close.
Would you not buy a car privately that you saw and wanted because you would rather go to a car dealer?

Yes some people may be too timid to inspect at a private sale.
Many people today also lack confidence in them selves and their ability and would rather pay some one else do the yards.

In fact the buyer of my property while negotiating used the angle that I am saving what ever dollars in agents fees so therefore I should give more away, well no not really because I priced the property accordingly and told him so.
I s'pose the advantage I have is that I have sold properties as an agent for others and have confidence in my ability as well as having an understanding of the pitfalls.

In reality the majority of Vendors have a figure in mind that they want to achieve at sale, then they add what the commission would be and expect to list and sell at that so they don't lose.
Well guess what happens, the agent comes back after a month and tells you you will have to drop your price because the feedback they are getting is that the property is too expensive. What do most people reluctantly do? Drop their price. They are not going to drop their commission to make the price more attractive...

Nothing against Real Estate agents, I have worked beside many and I know what they do and how they operate. It is tough and competative, they want to sell the property to make a living, no sales, no income!
Most agents work very hard and deserve a chance. They are betting on their own abilities to survive, no free lunch, maybe a small retainer to assist if they are very fortunate.

For me, I guess I am reluctant to pay an agency $20,000.00 plus advertising costs to answer an occasional telephone call, put a photo in their window, then stand around my house greeting people for 45 minutes after I have spent 2 hours cleaning the place to present it. They can also lose a sale for you too if they just don't do their job well.