When getting a new badge, the earned badge button is clickable and opens the badge page:
However, when gaining new privilege, the privilege isn't clickable. Would be nice to make the privilege block also clickable, e.g. in the below example make the text "Edit community wikis" as link, and after click it will open Edit community wiki. Or, at least, open general Privileges page:
I agree that a link from the name of the privilege is important, and can be useful with each of your scenarios.
Linking it to the description of the privilege:
When a privilege is earned, users don't always know what it means, or what can be done with it. To use your example, and my experience, the privilege to "Edit community wikis" doesn't make sense if we don't know what a community wiki is or why we would want the ability to edit it. A one-click link to the description would be very helpful.
Linking it to the entire privilege list:
This gives a sense of where that privilege falls in the list, and an opportunity to see all the privileges at the same time. From that page, it's easy to link to the individual description pages.
Though I like both suggestions, my preference would be to link to the list. One basis is that the level of rep needed to reach privileges is different on graduated and beta sites. Compare the list on a graduated site, such as Travel, with the list on a beta site, such as The Great Outdoors.
One example is the "Cast close and reopen votes" privilege. Using the same two sites, Travel which is graduated, requires 3,000 rep, while The Great Outdoors, which is in beta, requires only 500 rep. That's a large difference, which can be confusing.
The specific privilege description page does say how much rep it takes to be awarded it, but it's under the title, and is in smaller print.
The system's offer to "Track the next one" links to a useful privilege page, but if we don't want the system to track it, that link becomes moot.
An obvious benefit, which looks to me like part of the reason for your question, is to create uniformity in the system.
