Having seen potential 1st round draft picks (such as Dickie Thon Jr.) make a lot more money by increasing their asking price, do you think a #1 rated draft pick could do the same?
If the player asked for $20-30M instead of the $10-15M that Bryce Harper and Stephen Strasbourg signed for, do you think he would be able to scare off the worst teams and be able to sign with one of the richer teams for a price that better approximates his market value?
There isn't much risk for the player to attempt to do. It would be difficult to scare off the teams with the top picks because they might not believe the player's asking price.