You wouldn't say none of them have not addressed the issue, because it means the same thing as all of them have addressed the issue.

You are probably trying to say this:

I wonder why none of them have addressed the issue.
I wonder why not any of them have addressed the issue.

These both have the same meaning, but none, here, works better than not any, for no better reason than it's simpler and therefore more common. But if you put the any next to addressed as you have it in your sentence, it changes the meaning a bit. Your sentence has the meaning I wonder why any of them have failed to address the issue.

p.s. Either singular or plural (none has or none have) are perfectly acceptable with none, despite its derivation from no one. You had no need to "correct" it to the singular.

You wouldn't say none of them have not addressed the issue, because it means the same thing as all of them have addressed the issue.

You are probably trying to say this:

I wonder why none of them have addressed the issue.
I wonder why not any of them have addressed the issue.

These both have the same meaning, but none, here, works better than not any, for no better reason than it's simpler and therefore more common. But if you put the any next to addressed as you have it in your sentence, it changes the meaning a bit. Your sentence has the meaning I wonder why any of them have failed to address the issue.

p.s. Either singular or plural (none has or none have) are perfectly acceptable with none, despite its derivation from no one. You had no need to "correct" it to the singular. Ditto for any.