It's just a narrative device, like a flashback. And we don't know until quite a way down the line that they're even connected. If you change the way in which the viewer learns about things that have happened to the character, does that actually change the nature of the character?

That wouldn't be a bad angle for stories - that's the sort of thing that creates dramatic tension.

A better comparison would be Watson to Holmes - Holmes is undoubtedly the star, but has a very peculiar mindset best represented by the experiences of the companion. Without Watson, Holmes wouldn't be very interesting, or interested.

OP, who cares? I mean, I know you do, but so long as the story works, why look for a formula? I like that the extraordinary life the Doctor leads will sometimes, even often, draw in anomalies who define his life and adventures for a time. Maybe Moffat relies on it a bit too much, so far, but the Amy/Rory/River arch mostly worked, and I'm intrigued by the Clara mystery. (Well, ok, I might not be wholly objective on the question of the latter being so superficially enamored by JLC that I half fell in love the second I saw her. But I think it's intriguing.)

RTD did seem to have his Doctors pick their companions solely on the basis of character, and if they turned out to be anomalies in space and time later on it had more to do with the Doctor having entered their lives in the first place. That worked too.

I've attached to only so many of the Classic companions I've seen so far though. Romana was great, as was SJS, IC, BW, SF (of course), Liz Shaw, Lethbridge-Stewert, and Leela (might be biased on that one too).

But Jo Grant? Peri? Those forgettable three who were there during the transition between 4 and 5? Why even have a companion if you're to make the fans suffer through characters like them? I guess the Highlander fellow who was with 2 was decent. But by and large, the classic cadre of companions, for all their "having been there and gone along for the ride" are a mixed bag.