After two companions who clearly fancied the pants off of the handsome Tennenth Doctor (pun intended), Donna is the bucket of ice-water in his cocky face. There would be no “reversing the polarity of the neutron flow” with Donna Noble around, she’d be far more likely to look blankly at the Doctor and insist he just gets ON with it.
And Donna wasn’t just there to act as a latter-day Tegan. The insane cockiness of the Tenth Doctor needed tempering. After Martha had been transformed from a trainee doctor to a soldier, and her family traumatised by the Master, he needed someone who could help him take stock of where he’d been and the rules he chose to live by.
Donna’s role in the Doctor’s life was similar to that of an elder sister, looking after a child prodigy. Yes he can do stuff that she can’t do, but she ping-pongs between knowing this is astonishing and being appalled by what it all means. And she’s not shy of telling him either.