I'd be fine with them talking, as long as it was not to critique the team in any way. Self critique is fine.
How do you think you played? I'd be fine with this. If the player mentioned another player, he would be fined heavy.
How do you think the team played? I'd be fine with this too. But again, no mentioning other players. Do that in house, during film sessions, behind closed doors. Break that rule, get fined heavy.
How do you think ______________ played? If you say anything negative about _______________ at all you would expect to be benched and fined.
The fines would be % based. If you make more money than someone else, your fine would be based upon a % of your game pay. Perhaps 10% for each comment. Say 10 things out of line, you play for free.
I would not allow the players or coaches more than 5 minutes with the media at any one time.
All fines would go to a charity of that player or coach's choice and any player who got fined would be subject to team discipline as well.
The lack of news would be hard on fans. Some fans who over react to every report need things to be hard. I could live with the silence, so it doesn't worry me one bit.