I perfectly like the current system and don't really see why you should change it. If your deck is no a no brain-playallthecharacters deck, you will find yourself not wanting to play anything the next turn sometimes, sometimes getting a ressource is the better option than drawing a card. So there are occasions, even if you don't even have a 11+ cost card where you'd use it, even if it costs 9. With people (imho unjsutified) puffying about call the warpath in another thread, i don't think it would be a good idea to make access to the 11+ cards more easy.
Most of them are more or less gamebreaking and also relatively rare. If they would be easier to play, you would not have to think much about using them anymore, they'd be an auto include for many decks. Because they are all epic, this could mean a bigger disadvantage for newer players.
Lets take a lot at those Cards:
The Calamity: Complete Board wipe, including commanders and with removal from the game. Also usable in every deck because it's factionless. Therefore you have to skip one turn but as someone stated before, you wouldn't want to play anything inbefore normally.
Subjugated Dragon: 22/22 unstoppable Flyer, Flyers are already relatively hard to deal with, but this guy also doesn't cost morale when he dies and spawns 4 6/6 new flyers. Also it's a verore Card, so you can easily afford to skip a turn very often, when there are no threads left to deal with after mass death in turn 8 or your opponent thinks you're playing mass death.
Dragon of Summer Flame: Flying, Unstoppable, Immolate 5 and kills the enemies defense zone over time. 24/24. You can play a herald in turn 10, while increasing your resources and let this guy charge in turn 11. Also as flame dawn, if you haven't won or lost this far in the game, playing more characters out of your hand won't help too much oftentimes, so you don't really lose anything if you "skip" one turn.
All those cards can even be cast easily without increasing your resources, even safely, if you drop the noble or BLBP the turn before.
12 Cost: Still realistically reachable with nobles only (for a secured play you need to save 2 of them in your hand)
Avarrach has Risen: Gamebreaking card, in many games this is kind of an "I Win" button. Sleepers also have the option of reviving their own or enemies nobles with hekeem or raise dead.
Hidden by clouds: Warpath has access to 3 different cards directly increasing resources (noble, Brings life by passing and Growth -> with 3BLBP in command, 12 cards) , a location lowering the ressource cost by 1 and Karani ( with 1 cost abilities and untapped wilderness you could increase your resources by 4 for one turn). Even if you Assasinate hidden, it will normally have spawned the next one out of the deck. After 2 turns, 1,2 or 3 beasts per turn come into play without any cost. Did i mention that the character is 35/35 and can block flyers?
Ao Shun: Not the best card in my opinion, but Indestrucitble, 30/30 unstoppable, flying and a card drawing machine. Dod can also often afford to do nothing for one turn, if their defence is strong enough.
Mega unit 02: Also pretty strong, but not completely gamebreaking. Also it's getting hard to play this one without increasing your resources.
Call the Warpath: Look in the other thread, not overpowered, but like Hidden, you can get to those ressources way easier in WP.
Virus of Avarrach: Literally gamebreaking, the game can't handle the sheer amount of tokens created oftentimes and crashes even on strong computers (dunno if already resolved). Kills everything and gives you a token for every character that died in the entire game. Harder to play than most other of these cards, Nobles could create a morale problem because they will be killed by this one. I don't want to see this in turn 10.
Maybe Scaling with the total resources you have would be an option; If you have under 10 ressources it still costs 9, at 10 8, at 11 9 again, at 12 10 etc.
But i don't really see that this one extra resource would benefit you too much in turn 10 most of the time.