It may as well just be taken as fact that Counting House is the "worst" card at $5. This doesn't make it a bad card, but it leaves it ignored in the kingdom most of the time. But because of what it does, it sits at an awkward spot in the cost continuum. Having a card yank Coppers out of your discard is a pretty cool effect, and can often be pretty useful. But because you start off with seven Coppers, Counting House has the potential to be worth more than double a Gold. So it has to be on the expensive side - you can't be able to pick it up en masse, and probably not on your first two turns. But since Counting House can also do absolutely nothing, such as immediately after a reshuffle, it can't be too expensive. Really, by rights, Counting House should cost somewhere between $4.5 and $5. But of course we can't have fractional costs.
So what could have been done to make it better? +Buy? Due to the best case scenario, that would have to shove it up to $6 in all likelihood, making it actually worse. What about an optional deck discard? Well, now you're just making the best case scenario happen EVERY TIME YOU PLAY IT. If I opened 5/2 with THAT Counting House, I would open Copper/It, and just start buying Provinces. Add King's Court and Scheme and you've automatically won.
Both Counting House and Chancellor have made me realize that a lot of the cards exist simply because there should be a card for their effect. They aren't there to be good or bad - they're there because they allow you to perform a certain Action. Not all cards can be Jack of all Trades or Count. So some cards exist simply for a narrow function that you may want to Marin into a strategy. And Counting House and Chancellor can both be useful (though I'd value the former more than the latter), most notably with each other.
That's all I got.