Can a new battery make your old iPhone fast again?

There's a rumor going around that you can boost the performance of your old iPhone 6 or iPhone 6s smartphone by giving it a new battery. The theory here is that Apple dynamically changes the maximum clockspeed on these phones, relative to the voltage output it measures from the battery. It's believed Apple introduced this feature to alleviate issues with devices that suffered from random shutdowns.

Basically, this means phones with old batteries will become slower because the lower voltage results in a downclocked device. Several folks on Reddit confirmed the behavior but it seems limited to the iPhone 6 series:

Anyway, apparently no one with a 5S has been affected here so far. Not sure why. I also found out a bit more about why this happens. Let me explain: Many people might remember that iPhone 6S battery fiasco, which for many, was fixed with iOS 10.2.1, and that seemed to be the end of it. Apparently, the way it did this is by dynamically changing the maximum clock speed relative to the voltage that the battery is outputting, so that your phone can’t draw too much power and shut down. I also don’t know for certain, but I believe that the iPhone 7 and up are not affected by this nearly as much, since the A10 and A11 chips have separate “low power” cores that apparently run at around 1/5th of the power of the main cores, and will use those as often as possible, and only kick in the fast cores when necessary, meaning you should only see slowdowns for more intensive tasks on the 7 and up, since only one set of cores can be running at once

The battery of these phones can't be replaced without opening up the phone so this can't be easily tested. Definitely an interesting discovery.