I don't know about that. Out of the original set, Jon Pertwee was always the most energetic and active of them all, and he was nowhere near the youngest. It all depends on the actor.
As for Rose, ugh... she hung around way too long. She was okay with Eccelstion, but with Tennant the love sick puppy routine got old very fast, and they continued the same thing with Martha. The best companion Tennant had was Donna. The interaction between them was great. Getting rid of the romance and just letting them be good friends reenergized the show. Reminded me a lot of Trouton & Jamie and Tom Baker & Romana, where they just clicked.