Pope was a reliable Republican with the approval of the Radical Republicans surrounding Lincoln, and he had had success in the West, particularly with his campaign to take Island No. 10. Compared to the Democrats in high command of the AoP, he was considered to be a viable alternative whose politics aligned with the goals of the administration. The Radicals wanted him, and so did Lincoln, so he was brought east and given command of the new Army of Virginia.
That command might have been more successful under the command of another officer. The question is, which one? McDowell? No, he had already failed in army command. Banks? Jackson had already proven him not competent to command an army. Sigel? Yikes--that's a scary thought. Franklin? Too cautious. Burnside? By his own admission, not competent, and also a McClellan loyalist. Hooker? Maybe, since he was a reliable Republican, but too junior at that time.
The other potential candidates were all junior, such as Reynolds, Meade and Kearny (plus Meade was recuperating from his wound during the Seven Days). And Fitz-John Porter, V Corps commander, was a McClellan loyalist who was court-martialed after the Second Bull Run Campaign to send a message to Little Mac.
At that stage of the war, there simply weren't many viable options. There was still too much political deadwood at the top, and the competent officers who came to the forefront of the Union war effort in 1864 and 1865 weren't ready yet or were still too junior.