Harpers Ferry sent out Cavalry to destroy Lee's pontoon bridges that were there. They had almost a week to move into position on the Virginia side. No way could Lee move 30,000 across during the flooding.
My point is that nobody expected him to get across as fast as he did. It proves a capacity to move faster than expected
It seems extraordinarily difficult to get beyond hindsight and existing dogma, just like with Antietam. Nobody is sitting with satellite images saying,
"Oh, the main Confederate army is just now reaching the Potomac" or
"Oh, look, they just today started construction of pontoon bridges and not 3 days ago, so we have time to deploy" or
"They only have XX,000 effective troops and no relief force is coming from Virginia."
They didn't have a week to know that Lee was for sure headed back into Virginia, at the exact same spot he crossed over the first time. I suppose the easiest way to more seriously answer the OP's question is to dive into what the Harper's Ferry garrison knew and when did they know it. When are they even conscious of this intelligence? Is there a one, two, three day delay? You can't just spread 10,000 troops in single file to block a crossing, you have to protect your own rear, you have to protect Harper's Ferry. How do you know Lee's not crossing somewhere else? How do you know for sure Stuart didn't cross somewhere else (like he did the first time)? One cavalry detachment starts harassing your rear area and the next thing you know you're the next John Pope dismissing a large force of the enemy as something else. You can't operate effectively with that number of unknown variables. You try blocking Lee at Falling Waters and a whole Corps might just wade across at Williamsport (like they
did), swing around, and completely wreck you and drive you away from your supply base worse than the battle of Winchester. Heck, maybe if they had have tried to have blocked the crossing that could have been exactly what happened. Meanwhile the Army of the Potomac tries futile and bloody probes of the earthworks defending the crossing point since the Confederates are still in them and not across yet. What a different end to the campaign.
Put one of the AoP's corps on the Virginia side of the Potomac and it's now in danger. You put a garrison there and it's probably worse and commanded by who?
Milroy?
The end results of the different battles and tactical situations are the result of enormous amounts of changing factors, you can only stray a little bit from the reality of what those were and be realistic without opening a huge can of worms and taking the time to measure each one of those worms four different ways to draw any conclusions.
The cost-benefit of the movement to try and block them is not without extreme danger. Just like attacking Lee's defensive lines September 18th, 1862. Just like attacking his lines outside Falling Waters July 13th. Both
could (and the last
definitely would) have been huge disasters.