The problem is, as DampeS8N alluded to in the comments, the Rebellion didn't control planets.
The Rebellion was organized into cells, some of which existed on most Core worlds, and which were openly accepted in many Outer Rim worlds - some worlds on the Outer Rim were so welcoming of the Alliance that they could be considered part of the Rebellion. Even these worlds, however, were still 'controlled' by their local governments.
Now to answer your real question, which seems to be "Why did the Rebellion warrant the construction of the Death Star?"
The Death Star was never designed as a weapon against the Rebels - though the Empire presented it that way - it was designed as a terrorist weapon to keep unruly planets in line. While a fleet of Star Destroyers could 'glass' a planet that wasn't as psychologically intimidating as a single, large ship that could reduce a planet to rubble in seconds.
BDZ - complete destruction of a planetary surface - took hours to accomplish and required a fleet of Star Destroyers. A defensive fleet around a planet, no matter how small it might be, would have a chance of destroying one or more Star Destroyers.
Not so with the Death Star - it was envisioned as being able to withstand any standard defensive fleet, could be escorted by a fleet of Star Destroyers if it was needed (such as an assault against a massively defended world), and could destroy a planet within seconds of reaching firing range.
If the Death Star were to be traveling the galaxy unrestrained the Empire could have clamped down hard, and anyone who rebelled would be swiftly crushed by their frightened neighbors, fearful that their rebellion would invite the complete destruction of their planet.
Tarkin said it himself, "Fear will keep the local systems in line. Fear of this battle station."
Edit: Made my answer to the asked question clearer, and clarifyed why I was discussing the Death Star