Yes they only had 1 base in ep IV. It is even in the text crawl at the beginning. "Rebels are striking from their hidden BASE".
Tarkin says he will end the rebels with ONE swift stroke. The interrogate Leia about THE hidden rebel base.
They only had one base and that was where all the leaders were. Hence why it is a win or die battle when the Deathstar arrives. It wouldn't really had any impact if the Death Star was just going to destroy Rebel base 053 out of 114 bases. But given how Rebels has messed things up, this might very well be the case now.
Episode Four was a mess from the beginning. The plot wasn't nailed down at all. Darth Vader is not Anakin, Luke and Leia are not siblings, and the official novelization cast the Emperor as a weak man controlled by his advisors. Nothing like what the series ended up being.
If you think an interstellar resistance movement that only has one base and a few dozen star fighters poses any threat to an empire that spans the Galaxy and has a military that includes tons of Star Destroyers, I don't know what to say. Why even bother deploying the Death Star when you could just jump a few Star Destroyers into the system and have them bombard the planet? There are certainly less design flaws that way.
The base is important because, as you say, the leadership is there. If you take out a cellular movement's central leadership, they would be terribly crippled. Possibly for years. Plenty of time for the Empire to focus on crushing individual cells before the organization can put itself back together. And besides, as per the Tarkin Doctrine, the Death Star being operational means it can simply destroy any planet even suspected of harboring resistance to the Empire. That's why the Battle of Yavin is important.
So in this instance, the new canon (and the old EU for that matter) is an improvement.