The important point isn't the micropayments, it's providing some sort of funding channel for an important piece of infrastructure that otherwise languishes.
In practice the model proposed for TCP/IP would not work because it's a decentralized crypto-currency.
In which case you're talking about consumables that have a high enough unit cost to "pay the price" of a single crypto txn.
Turns out we have this already! It's called bitcoin. Maybe you don't want to change your prices all the time so a new coin could be good on that end (letting markets manage the service cost). But that's just mental gymnastic, especially since ultimately everyone is pooling from fiat for a while (who's getting their salary in BTC or ETH?)
Also, plenty of companies in the space pay salaries in BTC and ETH. Check out BitWage for a provider.