Don't death row inmates get the most exhaustive appeals process of practically any class of prisoners? Honestly if I were innocent I think I'd prefer to be on

Don't death row inmates get the most exhaustive appeals process of practically any class of prisoners? Honestly if I were innocent I think I'd prefer to be on death row which has the most costly (to the state) and exhaustive of all the appeals processes. This change could counterintuitively condemn more innocent people.