Bitcoin: A Peer-to-Peer Electronic Cash System
As you said, any two parties are able to open (and close) a channel. However, these actions require an on chain transaction, and your funds are locked until you close the channel. Unless you're going to be exchanging many transactions in a short period of time with your peer, you would be better off creating transactions directly on chain.
I won't get into this here, but the lightning 'network' has its own set of scaling problems, which imo are much worse than that of the bitcoin network itself.
It's not technically a payment at that point, since the payments is atomic end to end. But yes, you send a message your peer, which sends it to another peer, which sends it to another peer...
like any other P2P network.
"A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution." [1]
Furthermore, the previous title was "Electronic Cash Without a Trusted Third Party" [2]. So reading "Peer-to-Peer" as "Person-to-Person" would mean that the title hasn't changed in meaning, it just became a bit more catchy.
Also, when analysing the incentives of participants in the bitcoin network, it turns out that network nodes do not actually form the ideal-typical p2p mesh network (where all nodes are equally distributed and connect to a few other nodes) but a more densely connected network where connectivity to mining nodes is strongly incentivised. This topic has been researched and discussed by Dr. Wright (See [3] for more information).
[1] https://bitco.in/bitcoin.pdf
[2] https://nakamotostudies.org/literature/ecash/
[3] https://nchain.com/en/blog/bitcoin-network-topology-small-wo...
Wrights comments on topology are technobabble and largely meaningless, so it's difficult to say something about them... however, to the extent that we can assign any meaning at all to them don't you notice that saying your transactions need to go through particular nodes sounds an awful lot like the property you're using to argue that lightning is not peer to peer?
Banks throwing away checks is not a problem. Bouncing checks are a fraud problem, which is why most everyone have moved on from using checks is many situations.
Lightning's solution is to just 'watch' everyone you do transactions with, which is a lazy, non-viable solution analagous to continuously watching an anonymous stranger's bank account when they write you a check.
It takes something that is, in human terms, relatively simple and makes it so convoluted that it's hard to even follow.
I read the Lightning paper and found it simple enough to understand (conceptually at least) how the channels are opened, updated, closed, and penalized. Of course the actual implementation is a more complicated and nuanced than what the paper covers.
The same volume without lightning would require blocks that were terabytes, which is obviously unworkable at the current state of technology.
A "black swan" event like a major lightning hub going down may force more channel closings than the network (as currently implemented) has time to process before time-out.
The LN simply does not work if the base layer is congested.