Also, most companions stay around for at least 3 series
Uhh, no; historically, the majority of companions have only stayed for 1-2 years. Only a few have stuck around longer -- Jamie for the Second Doctor, Jo for the Third, Sarah Jane for the Third & Fourth, K9 Mark II for the Fourth, Tegan for the Fourth (barely) & Fifth, Amy & Rory for the Tenth. (Romana, the character, was there for three seasons, but the actresses who played her were there for one and two seasons respectively. And Ace was a companion for two short seasons plus one serial, so that's barely above two for her.) True, some of the new-series companions have come back in later seasons, but that doesn't count as continuous tenure as companions.
In fact, the only companions who've stayed longer
than three years were Sarah Jane, who was a companion for three and a third seasons, and K9 if you count Mark I and Mark II as the same character.