If you broke two inches off yourself , would your performance be affected ,?
Which two inches are we thinking of?
With rods, there are at least two different ways to think about this, and another which involves the interaction of the two.
One, chopping a couple of inches off must alter the mechanics ie the way it picks up line, bends under load etc. There can't be no difference, but there might not be much.
Two, like a scratch or a dent on a new car, or a crack on the phone screen, it will bother some that the integrity of the thing has been compromised.
Three, even if the difference is small, some people might just not fish as well or enjoyably with a bit snapped off. I'd be in that category. Gear doesn't have to be the best, the dearest, the rarest, the shiniest ..... but I have to like it and not feel it's damaged. Even if I made it myself from bits chopped off other rods. so it would affect my performance, which trumps the rod's performance.
Wonder what the OP thinks of these answers.