The film's official novelisation is pretty clear on this. Tarkin, a man known for his decisiveness and with a penchant for Gordian Knot cutting made a snap judgment that the situation had deteriorated beyond reasonable control. He was also quite keen to test his new toy and kill some of the Admirals and Generals who'd proven an annoyance to him during the station's construction.
The deck shuddered lovingly as the battle station dropped out of lightspeed. Dozens of objects flashed onto the overbridge’s tactical
displays—Imperial and rebel vessels in conflict throughout the
system—and Wilhuff Tarkin made his assessment after seconds of
perusal. The Empire was losing over Scarif, but that was about to
There was proud enthusiasm in General Romodi’s voice. Tarkin looked to the old warhorse, then shook his head. It might be amusing—even illuminating—to test the station’s capabilities against a rebel armada, but now was not the day to toy with the enemy. Director Krennic, General Ramda, and Admiral Gorin had all failed to solve the problem at hand, granting the rebels opportunity after opportunity to seize the schematics from the Citadel.
At last report, the data vault itself had been breached. It was a show of incompetence so great that Tarkin was almost curious to know how Krennic might explain it away.
No. Best to start fresh—to eliminate the threat of the rebels, however slight, and clear away the deadwood of the Imperial military.
Tarkin looked to the viewscreen and to Scarif: an ocean-drenched sphere of islands rich with rare metals, useful as a construction outpost and research incubator away from the Senate’s prying eyes. But Tarkin would not miss it. Over the years, too many officers had treated it as a place for unofficial retirement; a tropical paradise where they could neglect their duty in comfort. The loss of the Citadel and the planetary shield would be a pity—but no more than that.
“Single reactor ignition,” Tarkin said. “You may fire when ready.”
Rogue One: A Star Wars Story - Official Novelisation
The film's junior novel concurs, adding that Tarkin has more concern for the plans than the personnel on the planet's surface.
“Lord Vader will handle the fleet. The plans must not be allowed to
leave Scarif—at any cost.”
It was then that the general understood exactly what Tarkin meant.
While the Death Star certainly could take out the entire rebel fleet,
doing so would require time. Every moment that slipped past was
another moment something could go wrong—something in the rebels’
Rogue One: A Star Wars Story - A Junior Novel