I think you are completely misreading the war.
Lee got stopped by General Stuart’s dismounted cavalry on day one.
Lee got stopped again by Colonel Chamberlain’s beat up 20th Maine regiment on day two.
On day three, General Longstreet, and I have to imagine everyone else in the general staff, was telling Lee to give it up, pull out, and find a new spot. Lee’s response was that he’d paid too high a price to leave now.
General Pickett, mind you, only took his orders. I don’t think he was happy to charge his infantry over a mile in open sight with the entire Union Army, and all of it’s artillery batteries, pounding on him with Concussive Rounds followed by Grape Shot meanwhile getting chewed up by entrenched Union Infantry behind a stone wall in the center, where all the Union’s communications were strongest.
So the question stands: Do Lee lose his bloody mind and make the most bone headed move in history, or did he have an ulterior motive?
Considering Lee controlled the battle field in every engagement he’d been in up until that point, I have to believe he had an ulterior motive. The only one I can think of that would be rational, is sabotaging his army to end the war faster (failed, if that was the intent, but it’s at least a reasonable thought to have.)
And, btw, there are TWO flanks to the Union Army. Since he failed at Little Round Top he could have either hit it with Pickett’s division while his own artillery batteries attempted to convince the union of a desperate charge up the middle, or hit the other while his artillery did the same thing. Both options may have given him the victory and were blatantly obvious. Although, the best decision would have been to withdraw, find his own high ground and wait for the Union to show up.