Cardboard recycling

I've said to West Wilts District Council:

Almost every time I take our cardboard to the recycling point (the one by Trowbridge College), the container is overflowing. This must mean that cardboard has such a low value that the District Council has to pay someone to remove it. On the other hand, cardboard must have a higher value than general household waste, otherwise there wouldn't be any point in collecting it seperately.

Therefore, by allowing the cardboard recycling bin to overflow, which means residents put cardboard in with the general waste, the District Council is increasing the council tax bill. Is this correct, or am I missing something?

I'll let you know what they say.