Lots of folks use graphic headers or logos on their pages inside an tag. The "href" of the tag is the current page on which the graphic resides.
They use the same header or logo on most every page of the site. The alt property is set with unique text for each page to reflect keywords that the page is optimized for.
If you've done any programming, you'll agree that programming must be precise. It is not forgiving like HTML.
Seems to me that using many different alt="whatever" properties for the same image would render all previous alt="whatever" as moot to a search engine program (or any other program). Only the last time the image was indexed would count unless the program was designed to set up an array of alt properties for the image and that seems a bit far-fetched.
So, my conclusion is that is not worth using tags on images for
seo benefit unless the same alt="whatever" is used consistently.
But it would be a whole nother can of worms if the image or logo was given a different filename. More...
A Real Doozey About The Alt Property! 
