A few things we've used to combat streaming:
1) As mentioned above you can make it a 6x6 league, making the additional pitching category a counting category negatively affected by innings pitched like Runs against, Ls, or HR against. That helps balance out the streaming gains in Ws and Ks with the downside in your Ls/HRagainst/Ragainst category plus the damage done to your ERA and WHIP.
2) You can set max moves however you want, but in the playoffs you can adjust each playoff team to 5 or 10 less than the max for each round. Say you have 50 max moves, you could adjust everyone's moves to 45 at the start of round one. With only five moves in the week, teams that rely on streaming are done. Then at the start of round two adjust everyone's moves back to 45 to give everyone 5 moves that week, and so on. Like I said you can discuss how many moves teams should get per playoff round, and whether the championship round should double to number of moves (since it's two weeks). Just make sure you discuss this before-hand so that everyone understands the new rules before they draft a team of streamers.
3) Make a rule that if someone streams, every other manager gets to punch said person in the junk. If it's a girl, then everyone gets one snip at her hair.