Except anyone can see that he did. He proposed an attack to be coordinated with an artillery bombardment. His 1864 letter faulted McClellan's timidity as to why it was denied.
So I'd like to make sure that I understand what, in your argument, Hamilton was actually saying.
So Hamilton's argument is that his divisional guns bombarding Wynn's Mill resulted in those works being
temporarily abandoned by the enemy, and by abandoned here what is meant that the enemy position was abandoned apart from a few men to work the guns.
Let's suppose that this is true, and that Hamilton's guns (amounting to no more than 18 pieces) drove the enemy infantry from the works into the woods in the rear. What this means is that the situation is as follows:
Position of Hamilton's front line is approximate.
Under bombardment by artillery, the Confederate infantry have abandoned their works, moving back no more than about 100 yards into the woods. They have also abandoned their barracks, moving back out of direct fire.
Under the circumstances that then obtained, this is a pretty reasonable course of action. Moving the infantry out of the direct line of fire and out of the works means that they are not opposed to attritional casualties - the Confederates are thus not taking the occasional casualty for no return.
More importantly, they have the means to react swiftly if Hamilton actually does try to take Wynn's Mill. The 15 mins marked is at marching pace (1 yard per second); if Hamilton advances, the Confederates have every opportunity to react and re-man the parapets.
In failing to realize this possibility, Hamilton is committing a failure of anticipation. He is failing to recognize the reason behind the enemy's actions (i.e. to avoid taking casualties for no purpose) and that they could modify that behaviour if it turned out that Hamilton was actually attacking, because they would see his infantry advancing over the clear terrain for a quarter of an hour before Hamilton reached the works.
In order for Hamilton's
assessment to be correct, that he could take the position with a single brigade, it would probably need to be the case that the Confederates had actually abandoned the works and that this continued after the bombardment had halted. This is because that would be the natural result if the Confederates placed no value on holding the works with infantry in the face of possible artillery bombardment.
The only other way in which Hamilton's assessment could be correct is if the Confederates were so unwilling to take artillery casualties (in their strong artillery works, which are as strong as the heaviest works at Dam #1 - the ones which meant that the troops sheltering in them took only a single-digit number of casualties from a long bombardment by the artillery of Smith's division) that they would leave the works unoccupied despite having means and opportunity to occupy them as Hamilton's division approached.
And if Hamilton's assessment is
incorrect on that second possibility, but a commitment is made as if the assessment was
correct, the result is a failed assault that runs into a heavily defended parapet after advancing over half a mile under enfilading artillery fire.
What I'm saying here is that, even if Hamilton meant for an assault combined with an artillery bombardment, what he had actually seen is not sufficient to demonstrate that the bombardment would have made the assault easy. He is imputing Confederate panic (or abandonment of the works regardless of the situation) when the information he has can equally well be explained by the Confederates wanting to deny him attritional casualties.
Bringing the