When selling by Private Treaty, the Seller needs to set an asking price.  Once a price has been set, it effectively tells the market the maximum the Seller will accept, and does not necessarily have any reflection of the property’s true value. It is a subjective figure based on historical sales which may have little relevance to the current market.

By marketing a property without a price and setting a date for the negotiation, the onus is on the Buyers to determine where they see value and put their best foot forward in a timely manner.

The property can of course sell prior to the day, on the day or after the event, which is determined by the seller based on the price.
In the case of it selling after the event, the asking price will be based on genuine Buyer feedback combined with other factors.