The purpose of the Master Emerald is specifically for Knuckles to have a sense of duty and responsibility that keeps him chained down, in direct opposition to Sonic's freedom.

Knuckles being chained down, unable to be free, is the entire point. He is SUPPOSED to be stuck in one place and NOT free to just be shoved in every adventure, because the entire concept is built on making him the Anti-Sonic. Sonic is as free as the wind, so Knuckles is the immovable mountain.

Sonic is not supposed to have a home, or a job, or any sort of obligation or even relationship that keeps him tied down. Inversely, Knuckles is meant to have all those things locking him down firmly. And so every new Sonic game takes place in a random new location Sonic just happens to travel to, but Knuckles being shoved in just to be part of the gang does not and can not make any sense because Knuckles HAS to be on Angel Island.

The only viable solution is to expand the scope of his guardianship to cover the Chaos Emeralds as well. As Guardian of the Master Emerald, it is his sworn duty to -also- keep watch over the Chaos Emeralds and ensure they do not fall into the wrong hands. The games previously trying to have Knuckles refer to the Chaos Emeralds as falling under Sonic's jurisdiction makes no sense. Sonic may be the one who embodies their power and can control it better than anyone, but it's not his responsibility. Knuckles' job as "The Guardian
should cause him to also be Sonic's Rival by having him be the "authority" and "master" Sonic has to deal with, which of course Sonic would rebel against.

Sonic is aligned with the Chaos Emeralds, Knuckles is aligned with the Master Emerald. Thus, Knuckles is the "Master" that has to keep Sonic, the "Chaos", under control and neutralize him if need be. But Sonic, like with SA1's theme, understands that "Chaos" does not need to be mastered as long as you open your heart, because the heart is the true master of chaos. Not the Master Emerald.