THE INTERNET happens in layer 3 mostly because layer 3 is where ROUTING between different networks happen.
Let's say layer 2.5. We have MPLS for 20 years now.
MPLS is actually pretty cool technology. It provides businesses with a VERY inexpensive way to create - effectively "nailed" end to end connections between buildings that geographically at great distances apart, but using the Internet as the mechanism for creating that "hard link' ... before the Internet was everywhere, the only way to get a true end to end connection between two buildings that were at great distances apart (California to New York for example) was to purchase very expensive dedicated circuits via T1 lines, T3 lines or fractional T1 lines also known as frame-relay circuits (those kinds of circuits were and are sold at a price based on cost per mile). T1 lines are the most common type and are telco owned dedicated trunk lines and they consist of 24 multiplexed channels of digital signal sent over two copper wires (64k in each channels because UNCOMPRESSED voice audio that happens in an end to end phone call requires 64k of bandwitch, so a T1 can handle 24 simultaneous phone calls). Of course when it came to interstate methods of implementing those connections on a physical layer, there could be any number of different technologies used along the way but in the early days before packet networks, infrastructure was optimized with multiplexers ... but with the adoption of fiber, other technologies were created to then transpose those kinds of signals on the fiber, but a T1 line from California to New York, had a government mandated level of service that we call the "Five 9's of reliability" meaning that as per federal law, that connection had to be up and working 99.99999% of the time in any given 12 month period.
Today, companies can have a very similar kind of service using MPLS. The difference being that MPLS uses the telco's INTERNET backbone to create a virtual point to point connection between two different buildings.
What is important to note here is that even though the packets that define the MPLS connection do exist on the Internet, the actual data that is passed within those packet streams ARE NOT accessible to the Internet. Because that MPLS connection is handed off to a customer as a point-to-point dedication connection that the customer would have to assign IP addresses to that are consistent with their internal PRIVATE network.
It's like VPN, only managed by the telco themselves and without any need for the customer to deal with VPN details such as usernames and passwords etc. I like to think of it as a tunnel but better than a tunnel because it has certain bandwidth guarantees that go with it and that bandwidth is managed by the phone companies who own that infrastructure where the customer has no control over that aspect of the link.
Here again, MPLS USES the Internet ... but is by no means a definition of the Internet itself... MPLS is to HTTP is to TCP is to UDP is to FTP is to SFTP is to TELNET is to TORRENTS is to etc. etc. etc. they all ride on the Internet but are not the Internet in it of themselves.