Speaking from the present-day perspective, I really don't like Doctor-light Doctor debuts. Their name is on the show, they're the one we're tuning in to see. I can conceptually respect the idea that the wider viewing public needs to be held by the hand and tricked into watching crazy science fiction by disguising it as a soap opera, but it's boring! Doctor Who without the Doctor (and associated accoutrements like monsters) doesn't work, because the show is developed around space adventure and time travel, not aimless young adults hanging out. It just turns into a lousy soap opera (or, in the case of "Deep Breath," a lousy period mystery show).
That Disney executive who suggested that scene of the Doctor almost getting smushed in "The Church on Ruby Road" was on the money, we need the Doctor involved as early as possible. They don't necessarily need to pull focus exclusively ("Smith and Jones" and "Partners in Crime" did well with having the Doctor in the first half of the episode while keeping a focus on Martha and Donna's status quo, and we already knew that Doctor and didn't particularly need to be sold on him), but the companion's relationship and rapport with the Doctor is the most important thing for the episode to establish (or vice-versa, in the case of "The Eleventh Hour" and "The Pilot"), not the friends, family, and co-workers they're about to ditch, and keeping the Doctor at arm's length just makes for a strange, aimless thirty or forty minutes of preamble before we get to the good parts.