That's happened in the comic too, right?
With Snively and Dr Starline instead of Stone though.
I think I'd rather have that too (Stone replacing Jimbotnik) rather than having new actor as Jimbotnik.
Actually quite the opposite!
Snively tried to usurp Robotnik a few times. Dr. Robotnik eventually outsmarted, defeated and trapped Snively in a prison pod and just left him there.
Dr. Starline was the one who "restored" Dr. Eggman to his evil self and was mentored by him for awhile until he tried to go it alone. Long story short, Dr. Eggman may have killed him.
As for the movies, to me it appears Stone is totally loyal to (and maybe gay for) Dr. Robotnik. He never made any attempt to usurp Robotnik, not even attempted to takeover on his behalf. Robotnik gave him instructions with that coffee shop and he followed through.