@Piedone (Hello!)
How the North Won: A Military History of the Civil War by Herman Hattaway and Archer Jones (University of Illinois Press, 1983, 1991) was a real eye-opener for me when I read it years ago. The picture,
based as much as possible on correspondence written during the war is pretty consistent and convincing that most generals - not only Lee or Grant but also some of our favorite goats like McClellan, Bragg and even Banks - were really trying to come up with imaginative solutions to the problems they directly faced. We tend to play the woulda-coulda-shoulda game a lot (heck, we're human and it's fun), but our memes are just that - easy to remember but oversimplified portrayals that actually move us
away from appreciating how tough it was to lead a nineteenth-century army in the face of politics, logistics, and the sheer impossibility of accurately predicting all enemy activity. It is true that some were certainly more talented and more successful at reading situations than others, but it is also true, as you say above, that it is "improbable that any general should have the goal to produce huge losses of life" or to deliberately set out to fail. (The way some campaigns are bitterly described by some (armchair) 'wishful thinkers' today, you sure wouldn't think so!)
From soapbox to sources:
"When Grant, his staff, Smith, and sometimes Sherman and Dana had been discussing future campaigns for the West and scheming to place their man [Smith] in command of the army of the Potomac, logically they also worked out a strategy for that force. Coordination between the armies of the East and West implied some specific campaign for Meade to harmonize and cooperate with those being considered for the West. The plan was not revealed until Halleck, in a January 8, 1864, letter which explained the military situation in other theaters, solicited Grant's views without revealing that they eagerly awaited them and would treat his ideas with respect. Grant promptly responded, writing one letter explaining his proposals for the spring advance from Mobile and Chattanooga and another outlining eastern operations.
"The plan was pure Grant. It prescribed a raid against the enemy's railroads and logistic infrastructure. He suggested that operations should 'commence at once by removing the war to a more southern climate, instead of months of inactivity in winter quarters.' To accomplish this he proposed that a force of 60,000 men start from southeastern Virginia, advance to the rail junction of Weldon, ruin the railroads, and then move south along the railroad to Raleigh, completing the destruction of the outer of the two Confederate north-south rail lines.... '...This would virtually force an evacuation of Virginia and indirectly of East Tennessee.' This major success would be made possible by seizing the initiative, drawing 'the enemy from campaigns of their own choosing, and for which they are prepared,' and by a surprise seaborne attack on a weak line or, as Grant expressed it, drawing them 'to new lines of operations never expected to become necessary.'" (Hattaway and Jones, pp. 511-513)
The Grand Design: Strategy and the U.S. Civil War by Donald Stoker (Oxford University Press, 2010), pp. 547-548:
"Late January 1864 saw Grant's first formal statement on operations in the Eastern Theater. He had habitually refrained from offering any such comments because it was not his command area and no one had ever asked him. But now Halleck was asking. Grant recommended shifting the focus away from Virginia by massing 60,000 troops further south. 'I would suggest Raleigh, N.C.,' he wrote, 'as the objective point and Suffolk as the starting point. Raleigh once secured, I would make New Berne the base of supplies until Wilmington is secured.' He saw many benefits here. First, he thought, it would force an evacuation of Virginia and, 'indirectly, of Eastern Tennessee.' This would open to Union armies untouched regions where they could 'partially live upon the country' while also taking potential stores from the Confederates...."
Now, of course, had this plan been adopted it would have run into its own difficulties and Confederate counter-moves, but what I hope this really illustrates is the bankruptcy of the 'all that ever occurs to me is to pound ahead with human waves' caricature when it comes to Grant. Other memes attached to other generals could also stand some questioning.
On another note: Coming at Richmond from the James was always the correct
military strategy, as McClellan knew back in 1862. But the worth of Richmond for both McClellan and Grant would be if the main Confederate army could be pinned there to defend against a siege. Then - and Lee knew this as well of course - it would be a matter of time.
(Well, sorry for the novella... that wasn't a pat answer at all, was it?)