With hindsight, it's clear that the optimal strategy would be focusing on naval superiority (capturing major rivers and ports) and fomenting/supplying Unionist revolts within the South in regions that were strategically important/easily defensible (West Virginia obviously, but also East Tennessee, South Texas, etc.). If they can free the local slaves sooner, even better for your cause. Critically, leave Virginia proper alone until the very end of the war (i.e. until you could attack simultaneously from the north and south), with just enough Union troops in the area to break a potential siege of D.C. if necessary. It's the most defensible area of the Southeast with all those smallish rivers and mountains and the martial culture gave the Confederates their best officers.
The Union had an overwhelming advantage in men and materiel so it didn't really make sense to abandon a theatre. The Confederacy would gain much more by sending Lee and most of the Army of Northern Virginia west than the Union would be attempting a strangulation tactic. So at best it lengthens the civil war by years, if not leading to a negotiated peace.
And even if we handwave strategic issues, it would have been absolutely politically impossible for Lincoln to tell the Northern public he was refraining from sending Union armies into Virginia because reasons.
