Tegan had her moments, but she could be quite grating sometimes. Most of the time.
I've heard it said that the old show never quite recovered from Tom Baker's departure. I think there's some validity to that, but I also sometimes wonder if it might be that the old show never recovered from Tom staying so long. I think there are other factors - JN-T could've used someone to rein in some of his wackier ideas, for example - but I do wonder if it might've been better for the show (and perhaps for Baker, as well) if he'd done only three series, as Patrick Troughton recommended to Peter Davison. That would've had him leaving around the time of "The Talons of Weng-Chiang", and would've allowed Louise Jameson to serve as a transitional companion. Properly written, Leela's reaction to a regeneration could've been priceless.
It's difficult to say, even with 20/20 hindsight, how things might have gone differently and what factors led to the show's eventual cancellation. Still, 26 years is a phenominal record for any show!
Which was the story (a fairly recent DVD release) in which the Doctor thinks he's going to get rid of Tegan but ends up being stuck with her again anyway? The look on his face at the end of that episode is classic!
For the record, I love brassy women and so I love The Mouth On Legs.
I know that she's mostly out of the acting game, but I would love to see Janet Fielding reprise the role. (A Tegan-Rose throwdown would have been mind-blowingly awesome.)