Do you think adding an edit option in each section of this screen is too excessive for the user?
Although in the world of coding, they always advocate DRY coding and not repeat the same line of code more than once.
In design its a bit trickier. You should never sacrifice usability for the sake of aesthetics. If the edit link brings clarity to the user, then perhaps you shouldn't remove it just so to make your interface cleaner. You would know through a series of user testing whether to keep the links.
However if you think the links make the site a bit too heavy, then consider these options.
A simple "Edit" indication by each title may not be too excessive at first glance of a simple view, but if you have lots of items, that Edit text repeated each time can start to be. Consider this,
Typically you want to avoid having too much repetitive content/elements in your views as much as possible. This will reduce your overall "visual noise", and makes things look nice and tidy with the clean whitespace.
UX designer Brandon Walkin says:
“The amount of visual noise in an interface has a great deal of impact on the perceived complexity of the interface.”
With that in mind, keeping the visual noise as low as possible with make the interface seem easier to use.
Here is the options I would go with:
Add swipe functionality. Following a common method used in modern applications today, as well as native functionality on some smartphones, this method makes it simple to clean up your interface by hiding content, and offers an intuitive way for the user to complete quick actions to an item without having to switch through multiple views. A drawback to this method is that unknowledged users won't have a way to know that functionality exists right off the bat, so having some tour or added indication may be necessary. Here is an example of the functionality used in the iPhone while editing Voicemails.
Add actions in the item view. If you are planning on adding additional functionality, a small swipe may not hold all of those actions. In this case, consider adding those actions in an item view. Instead of going directly to editing an item from the master view, nest the edit action within the item view. This will give the same visual affect as the swipe method, but allows a more scalable solution to add later functions. This is how the caller info view is setup when the user clicks on the info icon from their Voicemails in their iPhone.
That's of course not all you could do, but those are my suggestions.