If I may be so bold, the Doctor's need to replace companions stems from the loss of Susan.
Susan, Ian and Barbara were the first TARDIS trio, the packaged deal. So, when Susan left, the Doctor was obviously sad. Vikki reminded him of Susan, so he adopted a new granddaughter figure.
Then, Ian and Barbara leave, the very two people who mellowed him out. So, wouldn't you be sad and want some new best friends after the people who showed you your humanity.
Of course, New Who shows the doctor going off the deep end when they don't have companions, but it's not about keeping them from going Time Lord Victorious.
They just really want friends. Not even to show off the universe or anything. They are just a people person.













