Anybody that thinks you can align a bullet straight on top of a case with your fingers is foolish. Fooling yourself and others. The main thing a seating die does is align the bullet before it starts seating it. The better the fit and finish of the seating die is, the better the seating punch fits the bullet, the better the final alignment will be. The case and bullet have to be held in good alignment with each other in order for the bullet to seat straight.
I think we are in agreement here, but to add some detail. . .
The purpose of the "stick" is that is how I know the case is belled enough that when pushed squarely, I know the bullet will not hang up on the case mouth going in.
The purpose of aligning it straight is to get it straight enough to go in the seater die and also to not hang up on the case rim.
Also, related to your bullet seater comments, I agree that Forster makes a good seater. Hornady is similar, but slightly looser I think Hornady is using the case for alignment where Forster is using the press accuracy to align the case to the bullet which by the nature of the seater is aligned to the die/press. I've made good ammo with each, but Forster is my go to for best quality ammo!
Frankly, I'm not sure non-bullseye handguns benefit from going the Redding route, but I could be wrong.