Short answer, nobody knows if the Death Star can jump into hyperspace fast enough for it to be useful at the Battle of Yavin.
So if someone asks George Lucas why didn't the Death Star jump into hyperpspace he can always pretend that they thought about of it while making Star Wars but the Death Star takes hours to program and jump into hyperspace.
Of course the Death Star always had hyperdrive:
"What is it?"
"The Death Star has just entered our star system!"
"What's the Death Star?"
"The ultimate weapon of the First Galactic Empire. And it's headed for Alderaan!"
"The First? Why, the Fourth Galactic Empire ended five Thousand years ago. What does some relic of the first one have to do with us?"
"Did you sleep in your ancient history classes? Alderaan was the first planet to revolt against the First Galactic Empire, and now the Death Star has finally reached us after all those millennia."
Obviously the Death Star must have hyperdrive capability in order to be an effective weapon in a galactic civil war.
The only clue as to the Death Star's speed of jumping into hyperspace is Vader's statement.
"This day has seen the end of Kenobie and it will see the end of the rebellion."
If the entire hyperpace trip from Alderaan to Yavin takes less than a day, obviously preparing to and jumping into hyperspace takes less than a day for the Death Star.
But nobody knows how much shorter than a day is needed for the Death Star to prepare and jump. if there is a canon statement that it always takes X number of jumps into hyperspace to go from Alderaan to Yavin then the maximum time it could take the Death Star to prepare and jump would be 24 hours divided by X. And of course the Death Star might be able to jump into hyperspace much faster than that.
But nobody knows if the Death star can jump into hyperspace fast enough for it to be useful at the Battle of Yavin.
And were the rebel fighters far enough away that they would be left behind if the Death star made a short hyperspace jump or would they be carried with the Death Star?