True enough.
However, it must be noted that in both cases the "living off the land" period was brief, and the armies were moving. A large army would "eat out" the territory for 10/20 miles in all direction in just a day or two. If it didn't keep moving, it would start to starve quite quickly.
This was a truly ancient limitation on campaign strategy, going back literally thousands of years. Armies could be adequately supplied using oceans or river transportation, if the logistic services were well organized. But without them, they ran into trouble very quickly indeed.
Of all pre-railroad armies, only the Romans and perhaps the Chinese seemed to be able to keep large armies supplied consistently overland. And I don't think we're clear on how they did it, though it was obviously a major reason the Romans built their famous roads.
In the Vicksburg Campaign, Grant rampaged around Mississippi, living off the land, but as quickly as he could he re-established his railroad and river supply routes. He absolutely, positively could not have besieged Vicksburg by living off the land.
After taking Atlanta, Sherman eventually cut loose and headed for Savannah, but he was heading for the coast where supplies would be available. He also kept moving. If he'd had to besiege August, for example, for more than a couple of days, he'd quickly have been in trouble.
One Union army did get cut off in Chattanooga after Chickamauga, and darn near starved before Grant reopened an adequate supply line.
I agree with you about the aggressor in the prewar period being the CSA. It is entirely obvious that Davis needed to change the equation in order to move the CSA forward. Lincoln only needed to maintain the status quo, and it is probable the untenable long-term position of the CSA would have become obvious and the CSA would have eventually probably collapsed, extorting constitutional protections for slavery to return to the Union.
To prevent that, Davis had to gamble on war bringing all the slave states into the CSA. He gambled and won half.
BTW, I think Meade doesn't get enough credit. He actually managed to outright defeat Lee in open battle, when the Army of Northern VA was at the height of its power. Nobody had done that before, and even Grant did not succeed in doing so, though very largely because Lee would not come out and fight him.
I do think Grant would have not allowed Lee to escape across the Potomac after Gettysburg without a fight, but the outcome of that fight might not have necessarily been a victory for the Union. The Army of the Potomac was pretty darn beat up, too.
Meade's low profile then and since has very largely been because he really, really pissed off the press corps, who made a pact never to mention him except dismissively. There's no particular reason we should honor their pact.
Recently finished reading Allen Guelzo's 2013 book "Gettysburg".
Guelzo doesn't like Mead, says he was a McClellanite who had no intention of defeating the Confederacy, would have been totally happy with a negotiated settlement -- live & let live kind of guy.
According to Guelzo's account, the Union won that battle not because of Mead, but despite him -- despite Mead's eagerness to retreat and reluctance to press his advantages.
And victory cost the Union some of its best officers, men who sacrificed their own lives to prevent Mead from throwing the battle away.
Personally, I think Guelzo has the right ideas here, and recommend him to you.