A bye can't win games, which even the lowest ranked player can do in theory. If you just want to find out who the highest ranking player is, then look it up in the rankings. If you want to find out who wins a tournament, let the players play.
If for technical reasons some players advance the first round without needing to play, then either make players earn that (I think I remember one could earn byes for MtG Pro Tour Qualifiers 15 years back), or make it random. Of course, being highest ranked is a form of 'earn it'.