Requested by Silke. (Here I’m responding a lot to Silke’s comment on having difficulty liking Martha.)
I’m actually gonna disagree with some of this. People always say it was a huge mistake to introduce Martha as someone who loved the Doctor immediately after Rose. But I think the thing is, the (Rose-loving) audience was predisposed to dislike Martha regardless of her storyline. I think if RTD had just ignored this, and just had Martha and the Doctor suddenly become the best of friends, this would’ve caused even more strife. Martha would be a “Mary Sue”, she’d be “replacing” Rose, the Doctor would be ~such a jerk~ for getting over her so fast, etc.
TBH I think it was very clever to give Martha the storyline she has because it addresses this head on. Martha isn’t replacing Rose. Martha can’t replace Rose, and Martha isn’t Rose. And the unrequited love story — in addition to setting up Martha’s overall character arc which I personally think is fabulous and probably the most empowering — sets up basically two tracks for viewers. If you like Martha right away (or if you disliked Rose), you can see the series through her perspective. It’s not like they intended for Martha to be unsympathetic. So you could sympathize with Martha, and realize how unfairly she’s been treating. If you’re rooting for Martha, that moment when she “gets out” is excellent pay-off and very empowering.
On the other hand, if you spend most of the season grieving Rose, like Ten does, and disregarding Martha, the story sort of allows that to happen… until the end, when Martha says “you know what? I am good, and fuck you for not noticing”. The Doctor is chastised, and I think, in theory anyway, the audience should be as well. Series 3 ends with the text saying, very loudly, “Martha Jones is amazing, she isn’t inferior to Rose, and you’re wrong if you missed that”.
People usually say it would be better if Donna had come before Martha, but Donna did appear before Martha, and it’s not like fandom welcomed her with open arms in “The Runaway Bride”. (Also, I find it highly unlikely Donna Noble would’ve been well-suited to deal with Ten in series 3 or that they’d’ve become the friends they could become in s4, but anyway.) Also consider that Rose’s return in series 4 had been planned for some time. If you’d had the friendship buffer in s3 and then introduced a story like Martha’s in s4, in the lead-up to Rose’s return, things would’ve been even messier, and the fandom would’ve been in even more of a ship war. (Relatedly, I have no idea what the game-plan was with hypothetical Penny, but uh Catherine Tate is a national treasure so I guess we never have to deal with that.)
I mean, the reality is there’s always going to be audience members who don’t connect with certain characters. But I think it was clever of the show to tackle the issue of missing Rose head-on, because it wouldn’t have disappeared if the show had never mentioned it, it just would’ve turned into this fandom-specific battle and destroyed a lot of the emotional realism in the show.