Cardboard is definitely recycled. It is a floating commodity, worth about $140 a ton right now. Many businesses accumulate and sell their cardboard packaging.
Glass is often ground up and mixed with gravel, which is then used for roads or concrete.
There's no reason to not recycle metal - scrap yards pay $$ for it every day.
I am not sure why plastic is hard to recycle. Plastic bags, yes. But containers can simply be ground up, packed in bulk bags and sold to manufacturers. The recycling company does not need to melt the plastic pellets - the manufacturer does that when they use it. Even plastic that is new, is bought as pellets.
It would be interesting to see some local recycling stats, from the Brady landfill, for example.