This makes a lot of sense. You use the example of Pickett's Charge at Gettysburg. I wonder whether this idea also applies to Grant's direction of repeated frontal assaults at Cold Harbor. In other words, Cold Harbor wasn't just an isolated clash of armies, but it was part of a campaign and a strategy of attrition and continuous contact, which over time bottled up the enemy?
I think we should distinguish between deliberate and accidental. I think Grant's manoeuvres and statements make sense if he was trying to win in "one fight", and it's a command pattern of Grant to underrate entrenchments (stretching as far back as Shiloh).
To clarify - if what Grant was trying to do was to wear down his opponent in attrition, there's no real reason for him to have moved south of Spotsylvania and in fact at least one advantage to staying there, which is that the greater distance from Richmond enhances the distraction effect of Butler's subsidiary campaign; when Grant manoeuvres he is, pretty clearly to me, trying to fight or turn Lee
out of entrenchments instead of keep up pressure. Grant is after all the one who initiates all the movements.
Grant's view on entrenchments was that they were bad for the men and a sign of low morale (hence why he didn't entrench at Shiloh, and his prompt attacks on positions at Vicksburg, Champion Hill etc). Within that constraint, what Grant seems to be doing is trying to find the right combination to break through the "low morale" Army of Northern Virginia each time his attempt to outmanoeuvre them is frustrated; it's certainly aggressive, but I think the
manoeuvres of the campaign (a series of movements around the flank to work closer to Richmond) aren't necessarily joined directly to the
assaults of the campaign (which are genuine attempts to win the campaign against a heavily outnumbered opponent, in the new situation the manoeuvres have created).