The best companion to the doctor is actually the one true companion. Clara. The impossible girl, and the writers of the show ruined her in how they ended her character.
Be warned spoilers may come and if you do not want to know them then jump in a tardis and time warp back out of this post.
Spoilers from here*—————————————
So Clara has always been in the Doctors life. She has in fact been a key factor to his success and now she is gone and the Doctor apparently has forgotten her. Or so we would like to think. But here we can see the Doctor being cruel in his failure to acknowledge her for what she is.
Though this cruelness with his companions we cannot fault the good Doctor nor can we fault the companions. As the Doctor himself has stated,” Some left, some were left behind, and some a very few… died.”
Well Clara is the only soul who has done all three. Though in the end we see that she left him behind, this is actually not true. The Doctor does remember her, still in order to make her think she has closure there is the idea that he is letting her run so that it can be said that she left. In all actuality the Doctor left her.
The cruel point being that now like the girl that lived Clara is cursed to be the girl that died but didn’t. Not only do we see her leaving but we also see the Doctor’s love for Clara and his reckless abandonment of allowing her to leave without telling her how much he loves her.
So back to the point of the good Doctor not remembering her. As we can see in the episode Hell Bent, the doctor tries to erase Clara’s mind but his mind ends up getting wiped. This is followed by Clara ensuring that the Doctor does not remember her as she flies off in her own TARDIS.
Well the trick has been pulled on her as the doctor who is always one step or more ahead of everyone else has used the excuse of not remembering her in order to allow her to leave but all the time knowing that the woman he now loves will never, ever die. He has allowed her no rest and when they meet again and I do think they will meet again before Capaldi leaves, he will show his love for her by finally allowing her to die.