See the thing is, Jessie, James and Meowth don't know that they are failures through the eyes of team rocket. Yea even if Giovanni fires them, Jessie would probably chuck a hissy fit at Giovanni, Giovanni will send a few of his goons to take the trio out of the HQ, take their uniforms and dump them in the middle of some deserted place. Then they will still try and gain Giovannis' trust back by capturing Pikachu and personally delivering it to him. The goons will refuse, Giovanni will come down with his Persain and Ashs' pikachu trying to break the cage. Still Giovanni takes the pikachu, forces it to do bad things or Ash and his friends will be captured. So pikachu is forced into bad things, Team Rocket gets their job back, Ash gets Pikachu back and Giovanni fires Jessie for betraying Giovanni in the first place. She goes off to contests, James and Meowth are put with a newbie.
Yea thats what i think would happen. Still I don't watch the anime anymore so I'm not concerned.