2) Perhaps securing the Shenandoah once and for all?
3) A victory at Bull's Run gives McDowell the political heft he needs to be shielded from political interference? A level of interference that will be far less than with Little Mac as there isn't anyone north of the Mason-Dixon Line more politically cumbersome than McDowell's OTL succesor?
4) Where does Little Mac go with McDowell in place? Commander of the "Army of Virginia"? Or "Army of the Shenandoah"? He won't settle for a corps command, can't command cavalry, and won't subordinate himself to Julius Caesar, much less McDowell.
5) With a victory at Bulls Run, and a conquest of Virginia in 1862, McDowell's position becomes invincible (there'd already be talk of "President McDowell"). Once Richmond falls, his appointment as "General-In-Chief" is assured. It's a question though whether Mac still has a job, or has been moved elsewhere (Charleston? Mobile? Wilmington? The West?). I wonder how far and how long the CSA can hold together should Virginia fall within a year to eighteen months of the war starting.
And if the South shunts more forces East to face McDowell, that means heavy consequences in the West, allowing Grant to kick serious ass a whole lot sooner. Even Rosecrans could gain major battlefield victories (as opposed to victories of maneuver) ITTL.