For highly competitive jobs, it's expected that you'll customize your resume, cover letter, and initial contact to the employer to which you're applying. When acting as a hiring manager, you can smell a no-effort application attempt a mile away, and it's a waste of your time (the person applying, and the person reading the application).
On jobs that are more entry-level and "first job" types, like your first job as a waiter, food service, sales clerk, etc., this is less important, but will still show effort.
When a person is unemployed, I agree you should spend the time wisely. Casting your net wide is not as effective, however, as targeting places you want to work. If you don't have a specific place in mind, it's a much more effective use of your time to either go to job fairs (and make a personal, face-to-face impression with a potential employer), or register with a temp agency and get side jobs while still having plenty of time to apply to permanent positions.