Someone flashing to the ball side short corner is as important as the high post against the zone. The corner 3 is generally not there unless the ball reversal is really crisp or the pass comes from the inside.
Most teams, including UConn, have a 4 out basic offensive set that is designed to create dribble drive opportunities for your strongest player or against their weakest defender. Those don't work against a zone. The basic formation for a 4-out actually puts each offensive player directly on a defender, making the defensive rotations a lot easier. Even if the passing is really crisp, the corner 3 will usually be a little rushed, making it a lower percentage shot, and the high post is usually pretty well defended.
The holes in a zone are at 45 degrees from the hoop either direction, and hose holes can be pretty big on ball reversals. I like 1-3-1 sets against a zone (like Geno does). Your guards end up being at 45 degree angles to the hoop, and the baseline forward can pin down the two block defenders, causing trouble for the defense without even touching the ball. This opens up the middle because the defensive guards at the top of the zone are having to swing further from side to side on the ball reversals, and the defensive center has to keep an eye on the baseline forward rather than just the high post. You even create driving lanes for the wing guards if they are decisive with the ball and the baseline forward is hustling to the ball side on reversals to occupy the low block defender. It also opens up the give and go off the entry pass to the high post.
UConn, at our best, had a good passing center like Knight, Voskuhl or Okafor that was basically just tapping the pass down to Donny, Freeman or Boone cutting to the block. You do that a few times, and those low block defenders will be staying very close to home, leaving the 3's wide open.
I also don't like the 4 out against the zone because the biggest weakness of the zone is defensive rebounding. It is hard to find someone to box out when you don't have a man to guard. That said, when the offensive has 4 guys behind the 3 point line, it doesn't much matter if the defense is boxing out or not, they will still get the rebound.