The key here is where the troops were coming from.
Many of the XIX Corps troops that were rushed up from the Deep South to help combat Jubal Early in the Summer of 1864 were a part of the Red River campaign in April 1864. Would these have already been committed if a push from SE Virginia was approved?
It's unlikely that the Heavies from Washington and other garrison units that joined the AoP to make up for Overland Campaign casualties would have been put into the field before campaigning began because they weren't in real life.
The Shen Valley also had military operations in the Spring of 1864, so there were no troops to pull from there.
The obvious source, then, for additional troops for this expedition was the Army of the Potomac. But sending troops from the AoP, with its significant numerical advantages over the ANV, violates military theory - it dilutes strength of one strong army to exchange for two prongs that can't support each other against an enemy with significantly shorter interior lines.
Also, there's no guarantee that a good commander could have been found to lead the expedition in the Spring of 1864. Burnside outranked everybody, and it's likely his IX Corps would have been the one to get the assignment in SE Virginia. People Grant liked in early 1864 who could be given an army based on rank, Baldy Smith especially, turned out to be duds. And Rhea points out that Hancock, Warren, Sedgwick / Wright all had uneven performances in the Spring of 1864. Ord / Terry / Sheridan weren't politically feasible at that juncture. So who should get the job?