Why do we need a "routing" process in Lightning Network?

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 ?