I think it is awfully naive to believe that these disputes won't be coming to streaming services in the near future. I actually think they could be worse. The problem isn't that cable and satellite have traditionally had little competition, the problem is the individual networks are basically a bunch of monopolies themselves.
If you need ESPN, or CBS, or Comedy Central in your lineup, you as a carrier basically had to bend over and pay what they asked for. Then you passed that cost on to the subscribers. The only thing saving the cable co here was the fact that they often had few competitors and switching was hard so people just paid up.
In the streaming world, the networks are still in the drivers seat. You are buying Sling or Hulu or YTTV to get stuff like ESPN or Fox. The problem for these providers is that the streaming market has been very aggressive on price and as many have mentioned in this thread switching services is very easy compared to the cable world. They can't just give the networks what they want and pass on the costs, or subs will just flock to the next service that hasn't taken the increase yet. Ultimately to stay a cost leader in the segment a streaming service will have to play hardball with the networks, and that often means some blackouts.