That's just silly.

Layer 0: point to point connection (can be radio, cable, optic)

Layer 1: IP routing (this is purely inside some kind of computer with many PTP connects attached)

Layer 2: TCP connection sessions (arguably Reliable UDP and the like can go in here)

Layer 3: Bitcoin (Bitcoin only needs TCP/IP)

Layer 4: Lightning/Liquid/RGB/Fedi/Cashu (needs Bitcoin)

DNS is found at L1, as a distributed DB of names to address.

Distributing addresses is a little bit of a funny thing. It was originally designed as 32 bits but it would be simple to extend this to 256 bits and never run out of 64 bit network segment values. There has to be some kind of notion of ownership of IP address ranges.

Given the protocol to make IP addresses unique per node and follow the convention of bigger fanning out to smaller. I haven't thought through that exactly but you can consider an internet without DNS very easily if you quadruple the bits.

Binding names to addresses could definitely be done on bitcoin chain.

I think within another 10 years Bitcoin can practically quadruple its block size and handle all the required data no problem at all without becoming too expensive to run for an average technical person.

No, the internet is just a protocol for routing paths between computers with multiple network connections. If you have computers with multiple connections, you have an internet. It is only a coordination problem how to allocate the addresses.