"Make me an offer" will shorten the distance between auctions and fixed price listings.

In random searches buyers may run across this item and find it interesting.  Among the search results is one or several which include this language and a link to make an offer.  Assuming the asking prices are within the logical range they’ll attract attention.  Sellers may then summarily reject offers as too low, counter or accept.  Transactions will begin to ensue and both buyers and sellers will in time better understand the other’s position.  In time potential buyers, now understanding the approach, may search categorically for it within their general criteria and in time more focus on material from negotiable sellers and in this way illuminate the path, now lost, back to the levels where buyers and sellers freely interact.  For the moment, prices are generally too high and buyers are often unwilling to pay up.  Opening the door to negotiation should help.
  

Whatever the outcome the introduction of “make me an offer” as an option will encourage dialogue and provide another basis for comparison among otherwise similar items.  Given the increasing amount of material coming to market providing a mechanism for offer and counter is a significant step toward providing the principal benefit of auction in the listing setting.

This said, it is easier for listing sites that encourage buyer-seller communication [those that do not charge a commission], to provide this option.  Nevertheless eBay charges a seller’s commission and effectively separates buyers and sellers so it's clear other sites could do it.

After two years of experimenting with it on eBay it looks to me like an excellent way to induce sales.  Some sellers will use it and others not but in time it will chip away at the logjam of mispriced material now overhanging the market.

At the end of the day it is the total of sales, not the total of listing prices that matters.