1. She Made The Doctor Better
A central question of the new Doctor Who is whether the Doctor makes his companions better or worse. Whether he makes them into better, more whole people, or whether he turns them into soldiers, weapons, and martyrs. What isn't as explicitly addressed is whether the Doctor's companions make him better. Whether they make him more whole, more happy. Whether they lighten the horrible weight of his soul. Rose made the Doctor better. He was a battle-hardened veteran, the loneliest orphan in the galaxy. Whens he left him, he dashing grin, he wore a blue suit if he felt like it, and he was capable of love and compassion. If Rose hadn't given him that, hadn't made him better, he wouldn't have been able to bond with Martha, or Donna, or even Amy, Rory, and Clara. The Doctor became more human for Rose Tyler. He became happier, and his soul got just a little bit lighter. If you go back and re-watch, you can even see that just being around Rose made the Doctor happier, kinder: better.
Conclusion
I once saw a joke about Rose thinking she was "special," when she was really just the latest in a long line. But Rose WAS special. She was the first companion in the new show. She was the first companion who wasn't interchangeable. And she changed the Doctor forever. She did all this by just being herself, by just being human. The one thing the Doctor could never be, Rose was. So maybe you don't like her, that's okay! I really dislike Martha! We all have our preferences! But for crying out loud, she was not a bad person, she was not a bad companion, and she did not do permanent damage to the show.