The Doctor never should travel alone and that has been made clear with all his different companions. The Doctor needs them to keep him level.
Doctor Who has had its fair share of companions throughout the years. Men and women have graced the TARDIS with their presence but their importance to the Doctor often goes unrecognized. Why? Because the Doctor isn’t one to openly express his feelings unless, of course, it is anger.
But each companion brings a new level of compassion to the Doctor. He falls in love with those who travel with him. Not in the romantic sense all of the time but rather that he falls in love with his friends. He wants to protect them and humanity as a whole.
The fear is that without his companions, the Doctor may be reckless and either bring about his own death or bring on the destruction of the world. When he has a companion at his side, he’s more likely to be reigned in.
Again, it is not always a woman that has this power over him. Even Danny Pink, who the Doctor hated, was able to bring him back to reality when he was killed and made into a Cyberman. The Doctor is able to recognize the pain that his human companions feel and it makes him more human by default.
Sometimes we the fans forget that the Doctor is, in fact, an alien and it takes him having crazy moments and a human bringing him down for us to remember.
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Hopefully Bill and Nardole can provide that same support for the twelfth Doctor that all the other companions did before them. Because without a companion, who knows what the Doctor will do.