So far in Star Wars: Rebels, the Holonet is just an imperial controlled/mandated news source that occasionally gets scrambled by dissidents to broadcast a pirate message about the naughtiness of the empire. That sounds exactly how I want my Holonet to behave in the GCW era.

Why did no one try to establish some kind of rebel holonet to avoid the Empire's naughtiness?

Most likely because the Holonet requires a lot of really really expensive satellites. They instead hack the holonet and broadcast what they want over the news. We see this in Rebels.

I really enjoyed that episode of Rebels. It was a local broadcast tower that apparently reached as far as some of The other nearby systems. The group needed to be on site, in the server room to install a security spike (some sort of pick to the broadcast's lock) before they could take over the broadcast.