Lee was smart enough to knew that winning was a long shot against the North (who had more of everything) and that in order to succeed he had to take some long shots. This was a long shot, one that missed.
Recall also that the plan included a long cannonade of the Union line which was supposed to wreak havoc on the part of the line that Pickett was headed for.
The cannonade over shot the target and the plan fell apart.
Also, if Jackson had been at Gettysburg and had suggested a move to the right, I suspect that Lee would have done so. Although Lee had great respect for Longstreet, when Longstreet suggested the move to the right, I think Lee held back, thinking that only Jackson could pull it off and that without Jackson, it was safer just to slam into the center.
An odd mixture of too much risk-taking and too much playing-it-safe. And yet, it might have worked.