I just rewatched where we, the audience, first meet River Song. It's the library episode from Tennant's fourth season, while Donna Noble is the companion.
I'll give him credit for planting the seed early for that particular story arc, So I can't exactly fault him for being particularly horrible as a writer. If only there's a way to reign him in from going completely bat-shit crazy with numbskull stories cough*dinosaurs*cough*inspace*cough*whatthefuckover*cough*cough
And yeah, Eccleston was fun to watch. The stories matched his ability to display an almost child-like wonderment of the cosmos, while not being campy. And yeah, from what I've heard, he was seriously burnt out by the end of the first season. I'd love to see him come back, but unless the BBC works some wonders, I don't see it either.