Commodity prices never drop to zero, no matter how abundant they are (assuming a reasonably free market-- government can, of course supply "free" goods, but the results are never pretty). The suppliers of the commodities have to make a profit, or they'll find something else to do.
Not only that, but there will always be non-infinite bandwidth and storage available to users, while anyone can create transaction spam essentially for free. So minimum fees remain necessary for non-priority transactions.
Check your assumptions.
1) We don't know what the future networks will look like.
No, but we do know the science of today. I'm not sure you appreciate the meaning of
infinite.
It's not possible to transmit information with perfect efficiency, unless, probably, using quantum entanglement. It's also not possible to store unlimited meaningful information within a confined space, never mind making it all computationally accessible. I'd say my statement is less an assumption and more an observation, unless of course you can show how it's reasonably possible to make use of quantum phenomena in ways we can't imagine today.
2) Commodity prices do go to zero for periods of time. Sometimes they rot in silos, and cost money to dispose of them (negative worth).
I think he meant go to zero permanently, or at least substantially long periods of time.