I would assume that you meant to say every team gets the first pick of the round. If you didn't mean that, well, the snake draft does allow every team to have a first round pick.
Personally, a snake draft is the only type of draft I have done. An auction draft would make every player available to every owner, which seems more fair. I mean, let's face it, in a 12 team league wiht pick #10, you know you have no shot at LT or Rickey.