If I'm wrong, correct me please.
If we simplify Lightning Network, it seems to work the same way as this simple unidirectional payment channel between two parties (although Lightning Network is a bi).
So we can simplify the payment process between two parties in Lightning Network as following:
(1) The sender and the recipient should simply create a channel and deploy the contract, and then the sender will indicate the recipient's address in the contract as the recipient.
(2) Then, any agreed number of off-line transactions will be made between the sender and the recipient, so that the address of the sender for each multiple payment is verified by the recipient.
(3) Finally, a settlement will be made via a chain transaction, whereby the recipient will receive the full amount of the contract.
In a first view, it seems that no need for "routing" process.
So, can we now ask that Why do we need a routing process to make a payment in Lightning Network?
P.S. I refer you to the Lightning Network website, where it is mentioned that:
"By creating a network of these two-part ledger entries, it is
possible to find a way on the network similar to routing the packets
on the Internet."
Note: The payment channels are composable, which means that If A and B have a payment channel and B and C have another, then A can pay from C to B. But the problem is that there is a financial incentive for intermediaries. Now the question is which one is more affordable?
(1) Do as above approach?
(2) A and C create another channel between them without paying to B and without the need for routing ?