Strategically speaking, putting all your eggs in one gigantic metallic spherical basket is counterproductive. Perhaps in its initial phase, the Death Star (boy, the Empire sure could have used an Orwellian touch when naming things) might have kept breakaway planets in line through intimidation. But by the time the station was operational, the Rebellion (the “civil war” in the opening crawl) was already in full force. Tarkin even tells his fellow generals that an operational station would “crush the Rebellion with one swift stroke.”
Which is lunacy.
The Empire has no understanding of how to deal with a nimble guerilla force or run galaxy-wide counterinsurgency. Just look at the military hardware they employ: AT-AT Walkers, for instance, featured in the “Rogue One” trailer, make absolutely no functional sense whatsoever. Moreover, a giant space station is a blessing for the Rebels, who can now concentrate on a massive target and become less susceptible to one “swift stroke” themselves. Plodding easily detectable giant objects that seem to take hours to power up a giant canon are easy to avoid.