What gets me is that of all of the companions the Doctor has had (or at least the ones known to us) I never really felt that there was as close of a connection with Clara as opposed to, say for example, Sarah Jane or Leela. Even in the 'New Who' series I think there was a stronger bond with Amy Pond than Clara. I get the whole "Impossible Girl" thing and that made for some interesting retconning of the Doctor Who history, I just don't think she was 'the one' to have caused the Doctor to do what he did in the finale.
The cynic in me can't help but think that the 'somewhat happy ending' with Clara was forced upon the writers to appease the Clara fans.
I think Clara's an avatar for a developing Timelord mind, the same mind that has been in every companion the Doctor has had prior to then, including Rose, including Amy, and so on.
The hint for that was 'The Matrix' reference in this last episode.
I'm of the opinion The Master' could be a Jekyll and Hyde of sorts, who can appear simultaneously to his Jekyll/Hyde Doctor's companion counterpart because he/she/it is a time traveler.
/OR/ The TARDIS herself has gained some sanity and actually IS The Master AND/OR Clara.
So yes, I agree. The bond isn't incredibly close with Clara, but she epitomizes what the Doctor is and has been looking for in a partner, which is longevity in a relationship - a long term partner and companion to play with and gallivant through space and time with for more than a couple years.
Clara certainly seemed 'up' for this, overly enthusiastic, in fact, but there's something missing between her and the Doctor. Something primal. Try as she might to kiss him, or to get him to kiss her in this last few appearances, she just isn't attracted to him in that form.
I wouldn't be surprised to see the next few years take the show in new directions of becoming a more adult oriented with potentially explicit sexual content in the next few years.
Also, with numerous appearances of the Doctor and his counterparts in and around the California/Nevada/Arizona area, I suspect they are setting the stage for an American version of Doctor Who.
We do, after all, have two TARDISes now, and one with a functional chameleon circuit.
Perhaps they are leading to the creation of a BBC America version of Doctor Who featuring the ladies and a more mature - middle aged man rather than an older or younger man? A love interest for the Master in whatever form she appears, and an opportunity for the Doctor to 'cross over' to the states to interact with his counterpart?
In any case, take the series in it's entirety - all 50 years for the lesson here.
The Doctor's repeatedly discussed how time moves differently for him versus others and how people 'lose their minds and memories' of world saving events merely a day later.
For the first time since Jack Harkness, you have an immortal, and for the first time you have an immortal who's actually learned over time from the Doctor and accepted who she is and merely wants to play a role with a time traveler. She doesn't seem to care who it is. She preferred the Doctor because he introduced her to the concepts to begin with, but since he's so antagonistically against long term companionship and prefers fighting monsters and evil over enjoying the sights, Clara /err/ the Master may be a perfect counterpart.
Now they just need a man.
Now would you watch that show?
An American guy + Clara's avatar in an American female form + Me traveling space and time in Doctor Who, America?.
I know I would.
Heck. I'd write myself in as that main character.
Then again. if I could choose my women and could go anywhere in space and time, it just might become highly pornographic. The censors would love me, that's for sure.
My advice is to not compare Clara against the Doctor's prior companions.
The Doctor's clearly changed from who he was with them.
Not just in form, but in age and experience as well.
So can his needs and desires for companions.
Just like yours. In real life.
Wouldn't you freak out to find out the man is real?