Suzy Lafayette super power
It doesn't hurt the gameplay. It's a decent special ability, but not overpowered. Here are situations that discourage or prevent action chaining:


She can't play more than one Bang! card per turn (unless she has a Volcanic),
Dueling is dangerous when she holds no other cards,
Mancatos are not playable unless someone is shooting at her (so not on her turn), 
Emporio, Dligenza, and Wells Fargo result in card draw, so do not trigger her ability, 
She probably would not play a gun that is a downgrade.


Situationally, she might also not want to use a Gatling or Indians if it might kill a teammate, or a Beer if she and her teammates are at full life, or a Panico if seated next to teammates.

While I don't see it explicitly in the rules, my group has always played that you can't play a duplicate card. The rules do say


  There is no limit on the cards you can have in front of you provided that they do not share the same name.


so there is no reason to think she could play a Barrel, Mustang, or Scope if she already has one. For weapons, the rules say


  If you want to play a new weapon when you already have one, you
  must discard the one you already have.


which leaves a bit of ambiguity about whether Suzy could discard a Remington to play a new Remington. (Is it a new gun if it's the same as the old gun? My group says "no".)

Suzy with a Volcanic is a dangerous combination, but she is by no means overpowered. Calamity Janet and Slab the Killer are also particularly scary with a Volcanic.