He can look at their stats.
That would be ok, but it gives him less control. fine by me.
I would limit the coach to the 20 players who received votes, and he would have to take the top 10
I don't think he should see any of the stats. If two teams go had to had for the first place on their conference, but one team has many players in the ASG, while the other is more balanced, and didn't get any participants. If the coach of the second team becomes the conference coach he'll have an advantage over the first team.
You are right, the same problem exist in national teams.