Note that you can still attack in the same direction if you pivot, but it's easier to shield stop, though you can do more things out of a pivot.
Being able to suddenly change from Falcon's insane speed to stopping on a dime not only augments Falcon's abilities to force reactions and respond to them but it allows you to space in neutral easier, particularly with aerials and grabs for shield stopping.
Shield stop nair is the main one you'll see, it lets you start at perfect positions and drift in either direction, or rapidly slow down if you want to continue forward. Shield stop uair, knee, and bair are also pretty great for this purpose, but you'll see them a lot less.
If you're dashing and see the opponent do something that will put them into a mostly set position at the end of the action, and it's a reasonable frame commitment (i.e. short hop approach or roll), then if you recognize you're in position, you can shield stop grab, stomp, knee, whatever to catch them as the piece falls into place.
Because throws launch people initially from a position determined by the person who grabbed rather than the one who got grabbed, you can use shield stops or similar techniques for stopping motion to have more control and give yourself a little more room onstage to continue a combo than if you JC grabbed.
Sure you can pivot for all of these things, but everything I mentioned is simply easier with a shield stop.
And of course, shield stopping with the intent to actually block an attempt to hit your out of your dash, or in any situation, can also be good.