The entire process can be exhausted and wrongful convictions still stand. I suppose that means part of the "process" - more informal than formal - allows for people to keep digging at something and push for a case to be re-opened, but that implies they had a critical view all along and if the conviction is overturned, maybe the critical view was always valid. Obviously "the system" isn't, and can't be, perfect. The window for criticism is always open.
Corruption exists everywhere. Conceivably some of government in NY, including its prosecutors and judiciary, are corrupt - even very corrupt. "Machine" politics aren't an urban legend.
Discussions on this site occasionally touch on the problems created by the examples set by people in charge in corporations, or in the CAF. Why would anyone believe that doesn't apply everywhere? Alvin Bragg openly vowed to "Get Trump". Who knows what mischief that set in motion among the people in the institution under him, quite apart from their own political leanings in a heavily Democrat-supporting jurisdiction?
If the system needs people to think it isn't rigged, it has to act as if it isn't rigged. It won't do to complain about the perceptions people take away when the appearances of impropriety are so manifest. The onus is on the system to be proper and look proper.