If you are having trouble at Rank 15, the problem is your deck. It’s not a problem inherent in the game, I reached Rank 5 using a deck with only 3 rares.
Since you added me, I watched some of your replays with Ziran. I think your deck would work a lot better with Argeon. Ziran is not a good general, and requires a lot of cards to synergise with her hero power, whereas Argeon just works.
You should consider replacing at the beginning of every turn. You barely do this and seem to run out of cards which means you probably want more card draw. Lkian or Sojourner are not expensive.
Card rarity is not indicative of card power. Sunstone Templar for example, is garbage, don’t play it. Play Azurite Lion or Windblade Adept. If you need more dispel than Sunbloom, use Ephemeral Shroud, Lightbender, or Repulsor Beast. Get rid of jank like Bastion and Eclipse and put some Holy Immolations into your deck.