This is a super interesting topic, but hard to give concrete examples of, because we often iterate on problematic designs to find good designs, and I don’t want to spoil future cards.
In general terms though, I’ve personally been quite interested in finding a way to fulfill the Beast Mastery Hunter fantasy of “Just me and my one life-time partner pet”. We’ve worked on finding something fun (for both sides) like that a few times now. No idea when or even if we’ll find a fun way to deliver that, but I hope to someday. That’s one of the blessings/curses of Hearthstone; we can often feel like there’s a kernel of a fun idea, but not quite find the right version of it, and so save it for a later set where we can iterate on it further, and keep trying to find the fun.
I’ll give you one concrete example in Rise of Shadows development though. Crystalsong Portal previously checked your whole deck for minions; it tried to form the basis of a no-minions Druid deck, to embrace the Balance Druid fantasy. However it proved to be too weak of an archetype with cards available so far, so would require putting so much power in that one card to try to carry the deck, that it was inconsistent and not fun. Instead, we swapped it to just check your hand, so that it could be used in an aggro/tempo deck that at least played a significant number of spells.