Some decks need certain cards, but there are decks that don't need particularly difficult cards to acquire. Face Hunter doesn't need any Legendaries at all.
Dragon Priest in particular is an expensive deck. You need like 2-6 Legendaries (Chillmaw, Ysera, then optionally some of the other standard ones like Boom, Sylvanas, Harrison, Voljin, etc), 4-7 Epics (Twilight Guardians for sure, Light Bombs for sure, Cabals maybe, BGH maybe). Most of the common cards you need are cards from deep Blackrock Mountain wings. The only deck I can think of that has more Dust in it is Control Warrior.
Most other common decks are not nearly as expensive though. Secrets Paladin can get by with just the Challengers (Epics), Face Hunter and Zoolock only need Rares. Mech Mage only needs Boom. Mid range decks are getting a little Dustier needing a few big Legendaries, but you don't need lots of cards to have success on the ladder.