Why Resource Destruction is Bad
Call of Cthulhu has a very interesting resourcing and payment system, which I find quite unique among CCGs. However, the beauty of the system is its own weakness. In most CCGs, resource destruction is an obvious design area to explore. However, given Cthulhu's very stringent costing rules, resource destruction has become an overpowered strategy, and one that is dangerous to the cohesiveness of the game.
A common way to alleviate the dangers of resource destruction is to have your resources combine into a pool, from which you can draw, in any way that you choose. In Game of Thrones (GOT), you count up how much gold you're producing that turn and then can split that gold among any number of cards. You can play one big card, or any number of smaller ones. In Magic: the Gathering (MTG), the land provides individual resources, but its still essentially a pool that you can split up however you choose.
Cthulhu does not have this. Cthulhu has a very structured one card per one domain payment system. You start out the game with three resources already attached, but you won't be able to play a 3-cost card until turn two. If you want to play two 3-cost cards, it will take you until turn four. Compare this with GOT where you can play two 3-cost cards on your first turn given the appropriate plot.
Another common way to alleviate resource destruction issues is to have alternative ways for resources to enter the pool. In MTG there are tons of artifacts, creatures, and spells that produce mana. If your meta is getting hit by resource destruction, you can play more of these cards to remove the problems. GOT doesn't have quite the same thing, however you'll never suffer quite as heavily from location destruction since you're always guaranteed to be able to get some amount of gold from your plots.
Once again, Cthulhu has nothing applicable or similar in its game. There are plenty of ways to add extra resources to your domains, but no way to help pay for a card without using resources. Again, this problem really comes back to the fact that there's no pool to draw from in Cthulhu. You have to pay for the card from the domain itself, and if that domain is empty, you're out of luck.
Cost reduction has the same problem. There is plenty of cost reduction, but it is not the same as having an outside source which can pay for cards or add toward the payment. The differences are small in practice, but become incredibly important when faced with resource destruction. Cost reduction doesn't help at all if you don't have resources in the first place.
Now these limitations are not necessarily bad for the game. In fact, the way in which the costing and resourcing system works is one of my favorite aspects of the game. However, it does mean that even though resource destruction is a common design area to explore, it is detrimental and dangerous to the stability of the game and meta.
In most CCGs there are a number of "advantages" which you would like to be ahead on. In Cthulhu specifically, these include card advantage, resource advantage, and board advantage. Board advantage could change at any moment based on any number of cards you play, from characters to character removal. Hand advantage will change constantly based on how much you or your opponent play. However, resource advantage is by far the most difficult to alter during the course of the game.
Aside from a handful of cards, there's no way to overcome the "one resource per turn" rules of the game. Which means that if your opponent plays a card like the Rip-Off, your opponent is now 3 turns ahead of you in the resource curve. And there's no good way to come back from that. It is for all intents and purposes a permanent disadvantage.
This is really the same underlying reason why Transient is essentially a failed mechanic. It was an interesting concept, but the temporary gain of the transient resource was never good enough to make up for the permanent loss in tempo on the resourcing curve. This was only exacerbated by the fact that the transient cards themselves were pretty crappy. It seems like they were balanced under the assumption that Transient was a benefit (like Fast or Willpower) instead of what it actually is, a detriment. Forgotten Cities began to fix this, but didn't get quite far enough.
Ultimately, the very stringent rules and restrictions in paying for and playing cards makes the resource curve very important, and critical to staying at pace with your opponent. This makes resource destruction incredibly powerful because it hampers your opponent with a permanent tempo loss in their resource curve.