They did for me and many people I know that use them. They allow proper airation.
All you need for proof is at the end of harvest take the plants out of the pots and look at the roots. Compare them to how much Loose soil is left.
If there are 2 plants side by side, using the same number pot. You will see the SP will harvest more.
You must know how to water a plant when using containers.
Have you ever noticed the circling in the Plastic pots? Have you ever noticed them in Smart Pots? I think not.
What I have noticed using SP's is my plants grow wider and not taller and lankier like they do in plastic containers.
I guess it all boils down to what works best for you. And Smart Pots work best for me.
The material is the stuff they sell in the garden center at Lowes or home depot. It is the weed blocker stuff they use for flower beds to block weeds from coming thru.