After a long time study of how StackOverflow in general behaves on this subject, I think we should actually extend the possibilities for closing questions as off topic for gold and possibly silver badge holders.
I do have currently a gold badge for cryptography & encryption but I can see this has limited effect on the site as most of the questions that should be closed are not duplicates. Currently hardly any cryptography related questions get closed at all.
I'll leave this answer as it invites informed discussion and a counter argument to above view.
Votes for this answer should still be for the old answer displayed below, which I do not support anymore.
The problem is that most gold badges are for popular tags, mostly languages and runtimes on SO. And the gold badge holders are not automatically experts on all the different techniques. This will lead to false-positives, that are difficult to reverse.
As an example: lets check my stats: I'm at over 600 for encryption right now and over 400 for cryptography. Nice, but after a lot of questions, not even near a gold badge.
Now almost all of the crypto questions are also tagged with a specific runtime; if they aren't they are mostly off-topic. However, not everybody with a gold badge for - for instance - Java knows much about crypto. So you get an "expert" with a gold badge closing a question that can be answered (or, reopening one that cannot be answered). And the actual expert is helpless; the amount of traffic we get for crypto questions is currently already too low to close questions, let alone reopen them.
Now I've just taken my field of expertise as an example; I do think there are many many of these "niche" tags and fields, and I assume (hopefully correctly) that most of the gold badges are for really popular tags. All in all, an interesting idea, but I don't think that this will work as intended.