One presumptive objection would be the effects of this on the child's self esteem. Sure, it may initially be tough on the kid knowing that his original parents did not want him. If a gay couple or a single man or woman wants to adopt a child they will just have to outbid everyone else. Also, there is a great black market of people selling their children or bartering them for hits of crack or heroin. This free market solution will all but eliminate the underground child market because the internet auction, with its millions of bidders, will bring a higher price for the child than the streets ever could.
Many people believe that there is a free market solution to every problem.
Abortion is no longer the exception, but another example proving the rule.