I have indeed enjoyed CCG week here on PT--thanks for the series, and I hope we'll see more articles on CCGs as they evolve and are released for mobile.
When compared with the other ccgs on mobile, HS has remained #1 in its genre in part because of its simplicity--Matt is totally right about that. It's easy to learn, it's not that challenging to keep up with, and (my personal biggest difference-maker) the cards do not have too much or too confusing game-text. All of that gives it a huge advantage over most.
But I also think a significant part of its lasting appeal is that its atmosphere--the visual production values--are just very satisfying. There's nothing confusing about the layout, the colors are very bright, and it just "feels" engaging in a way that most ccgs (most apps, for that matter) do not.
Mrghol makes a point that I've heard a number of high-level players make--the new material doesn't come out frequently enough. As a more casual player, I don't feel the same way, though I admit to finding myself drifting away but then checking back in when new cards are being released. I think the solution might be to release the same number of cards, but over a slower period of time. Imagine new, UNLeaked cards that players can't prepare for, being released a few cards per-week for a couple of months. That would add serious life to the game and force the meta to constantly evolve, week by week.
As it stands, the reasons the game doesn't continuously engage me is that there's too much RNG (which will never change--the luck factor is part of what makes it so appealing to new players), the successful deck strategies are far too narrow (as Matt noted), and I find a handful of the Legendaries to essentially be silver bullets--they win games on their own regardless of deck synergy. Apart from being boring, they undermine real strategy.
I plan on trying Shadow Era (which I'd forgotten about--thanks Mirefox!), and I hope some new ccg emerges to challenge HS and push Blizz to make some changes that would improve the game.