That isn't really what causes the problem. Payments don't need to be inside the network layer of the internet.
The problem is that a digital payment system that works like IP routing doesn't exist at all, even independent of the internet. Existing banks could implement it trivially -- you walk into the branch with $100 in cash, give them the money and they give you a secret passphrase. Then the banks talk to each other so anyone anywhere in the world who walks into another bank and has the correct passphrase can get the money.
Except that there are laws against that. Know Your Customer laws that require them to know who you are and know who the person you're sending the money to is, even if what you're paying for is both legal and private. "Consumer protection" laws that require them to allow you to reverse the transaction, which means they can't just give the money to the other party, they have to sit on it for a while.
The effect of these laws is to make small transactions between random individuals incur prohibitively high transaction costs and subject honest people to capricious denial of service attacks by risk-averse financial institutions without effective recourse. It also makes people afraid to pay for things they don't want an official record of them consuming, which specifically applies to political speech when your views don't align with the party currently in office -- or the party who may be in office next year.
In other words, it interferes with people actually paying people for creating content on the internet. That leaves the creators with only advertising to support them, which implies central control by the ad network.
Fixing that requires a way to anonymously, irreversibly send small payments with low transaction costs. Which is currently de facto prohibited by law.