There are some complications to the implementation of this system. If you choose to incentivize the Realtor to stay below a specific budget, the Realtor might start steering you to cheaper units (re: smaller, shabbier, poor neighborhoods) in order to get a bigger commission. If you base the commission on the discount negotiated off the list price of a home, you may push the Realtor into low balling offers and not closing deals (not to mention, in many markets, homes sell for over list price).

Probably the best method would be too use a flat fee, or a percentage of list, and then add bonus commissions for performance in negotiations, using the average 'over/under asking price' in the local market as an index. But this is probably too complicated for most people, and at the end of the day, the Realtor is more concerned about the volume of deals they can close rather than the individual deals, so performance based commissions will still probably have minimal impact on behavior.

Unless the US market is very different, I thought it was pretty obvious that the sellers/landlords are the real estate agent's customers and the stream of prospective buyers are the product...

Because most real estate purchasers aren't sophisticated enough to manage their end of a deal like that well.