Having used two iPhones over the last five years, I've experienced many upgrades.
My first was an iPhone 3G (not 3GS), and through three iOS upgrades, performance didn't slow down because of the OS. Performance slowed when the apps updated themselves to newer versions and assumed everyone had the newest shiny phones---not Apple's fault.
My second is an iPhone 4S. Over 3 iOS upgrades, now, performance hasn't dropped by any noticable degree except for, once again, when apps individually update and assume they are only being used on iPhone 6s.
I would like to see evidence of this "well-documented" phenomenon because I don't see it in real life.