A saved search that you cannot easily re-run is just a record that you once had an idea. Checking what one currently matches meant rebuilding the query by hand in the search form.
Clicking a saved search's name now opens Company Search with that query loaded and executed. You see today's matches immediately, adjust the query, and save it back.
The list and the edit form were rebuilt alongside, so creating and tuning searches no longer costs a page load per change. Bulk enable and disable makes pausing a group of searches — during a domain warm-up, say — a single action.