Let's be clear: Halleck wanted to unite the two armies of McClellan and Pope. Rightfully knowing Lincoln's view on protecting d.c., and that no one had a viable second solution, how can you fault him for doing exactly what he did?
Simply by being at Harrisons Landing McClellan was preventing any major attack being made against Washington, and Pope's force was substantial enough to prevent a one-corps attack from capturing Washington. Reinforcing McClellan's forces (at any point in July) with the troops he'd been promised in the last couple of days of June/first couple of days of July would prevent any detachment of force sufficient to really threaten Washington.
The extra troops would permit McClellan to advance with greater safety than if he didn't have them.
That Halleck wanted to unite the forces of McClellan and Pope is not in dispute; what I dispute is that it was the only option. Perhaps it was the only option which Lincoln would countenance, but weeks previously Lincoln had countenanced promising McClellan as much as 65,000 troops (we have letters which demonstrate it); what good is the general-in-chief if he can't even fulfil one quarter of what the President has previously promised for fear that he'll be fired?
Of course, Halleck's plan has a greater flaw - see the next post.