You can't absorb things without absorbant mass. The black plastic sponge has hardly any mass at all, period.
I however do not have a good solution. I've DIY'd my own filter with charcoal pellets, but I've been unable to test it, and I'm somewhat unhappy with the design anyway.
I don't doubt you at all that cheap filters work less well, but at the same time, what are the consumer-grade commercial purifiers that aren't using cheap charcoal filters? I don't think I've ever noticed an in-store purifier that took pellets, but maybe I missed something.
Edit: it does make me curious if with a Corsi-Rosenthal box you could hang a non-enclosed/mesh bag/basket of charcoal pellets under the fan inside of the box and if that might produce better results than attaching charcoal filters to the sides. The obvious problem that springs to mind though is that this would make the design a lot more complicated and annoying to build. Might also result in charcoal dust spread around too, which might defeat the purpose of a purifier in the first place.
Unfortunately it seems like the air filtration market as a whole is incredibly prone to snake-oil claims.
As far as your idea goes, I'm not sure. And I don't have a great idea of how to test something like this. I've seen bags of activated charcoal marketed as something you can leave around for better air (sounds like bs).