It is possible to claim mistral on grounds of your public defender being unsuitable/inexperienced/incompetent/biased against you.

The problem is, what do you end up getting to represent you in the appeal trial? A public defender.

Who is
a) likely reluctant to move against a potential colleague
b) wary you'll do the same to him. c) just as incompetent

You then incur further wrath of likely the same judge as you go over the same material, as the judge dismisses anything new and the outcome ends up the same.