A demo is simply a series of screen shots lined up in a row and played in order. Therefore, by taking demos while you play, then playing one back when you recall a worthy moment (or looking for one while you're not playing or spectating) you can snap a screenshot as you see fit.
Your argument is akin to telling a digital photographer, "Don't go wasting all those shots, just pull the camera out when you see a good one." Digital (demos) is cheap, fire away, crop out the crap and catch those moments that you would've missed by reaching for the screenshot key.
Plus if you have a truly wonderful game, you can share the whole thing instead of "This is the screenshot I took just after the rant got past me, but you can't see it here..." Uninspired mass production would be gathering people together to pose for shots, telling them to start over when it didn't work out just right.