I think you are coupling a centralized voting system with one that gives equal access, and I don't think that's necessarily true. Being a centralized system makes it consistent, but not necessarily fair.

An independent body could be easier to undermine (single point of attack), and be just as likely, if not more likely, to reduce voting access across the country all at once. I think we'd have corruption either way. The inefficiency of the decentralized system could be slowing it down.

I think you are looking at the system with hindsight and assuming that because the current system is suffering problems, that a different system wouldn't suffer those same problems. I don't think you can justify that conclusion