I think that this is an interesting enhancement idea.
For the short term, know that you can "Save & Share Results" from the Save menu / button of the search view. This actually persists the search artifacts (results) of your search, and you can publish the link to your colleagues. Because it's just referencing the contents of a search which has already run, the time frame for the given report is "frozen", but the search bar's contents is the content of the search string. This allows your colleagues to then re-run the search on their own, but over a different time frame if desired, giving you the best of both worlds. They can use your initial search (cheaply--it's already been run!) as a launching point to continue their own search.
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