I think this is a fine idea for a variety of reasons. It intentionally harkens back to the original teacher Companions of the First Doctor. More importantly, it gives Clara something to do or someone to relate to other than the Doctor, appropriate given her shift from Eleven to Twelve.
I hope that "relation" isn't necessarily a romantic one, though. And I hope that it doesn't mean excessive attention paid to the Companions, vs. the guy the show is named after. While the Companions are there to ground the Doctor and create relatable characters for the viewer, I, at least, am there to watch the Doctor, not his sidekicks.
It would be amusing, briefly, if the inevitable twist were that Danny crushed on the Doctor, instead of Clara.
Speaking of Clara, is it established that her mucking about with the Doctor's timeline was focused only backward, not forward?
Reshared post from +Doctor Who TARDIS Crew
Meet Danny Pink, the new companion for Series 8
// bbc.co.uk/blogs/doctorwho/articles/Rising-Star-Joins-Doctor-Who-for-Peter-Capaldis-First-Series
I miss having companions that weren't contemporary humans. Ah well, maybe that will be the next one.
+Brittany Constable A good point. River and Jack might fall into that category, but all of the main ones in the new Who have been from "right now." It would be good to see something different. The "Wow, the modern world is like confusing magic" or "Wow, the modern world is like the stone age" routines could get tiresome fast, but, then, they run into the same stuff with contemporary Companions traveling to the future/past all the time.
Bah! Spoiler alerts, please, sir! I just finished season 6.