but I've never figured out why the show was popular and lasted so long.

It hasn't. It had a (generally) good run from 1963 to 1989 when it was cruelly culled by a cynical BBC. I think anything that came afterwards is referred to by the faithful as Nu-Hu (New-Who) to differentiate from the original continuity & the mythos thereof in which we might still imagine what the world would have been like if Geoffrey Bayldon had taken up the mantle thus depriving the world of Catweazel. Nothing in Nu-Hu can compare with this, much less the Weirdlore Zeitgeist that gave us The Daemons in 1971 - though I must confess to hiding behind the sofa when the morris dancers came on.

Enjoyed the Sarah Jane Adventures though; back to basics with character & story development rather than bogging itself down with big meaningless concepts and mawkish overkill.

Here's my vintage CYBERMEN just to show I'm a real fan of the show.