Yeah, but think of how many stakes you can make out of those felled trees!
Assuming a level surface where there's no slope that'll make a ball travel farther in one direction than another, it won't ricochet farther away than it would have gone if you missed the flag because of basic physics. You can't get more out of a collision than you put in.
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I personally like putting with the flag in; it saves me time (not a ton, but when I'm playing alone and trying to get done before dark, I never bother with taking out the flag, save for the rare birdie putt), and the math says I will putt better because of the help. I think this rule as stated will lead to a lot of messing around, but I wouldn't be opposed to the earlier suggestion of having the flags be fixed to the cup so they wouldn't move on their own or be player removable (I'm assuming the groundskeepers would want some locking mechanism as a way to get the stick out for maintenance and moving hole locations).