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

If I'm wrong, please correct me.

If we simplify Lightning Network, it seems to work in a similar way to this simple Unidirectional payment channel between two parties. (Although, Lightning Network is a bidirectional).

So we can simplify The process of a payment between two parties in Red rays as follows:

(1) The sender and the recipient only need to create a channel and implement the contract and then the sender places the address of the recipient in the contract as the recipient.

(2) Then, any agreed amount of transactions outside the chain will be made between the sender and the recipient, so that the address of the sender for each mico-payment will be verified by the recipient.

(3) Eventually, a settlement will be made through a chain transaction, through which the recipient will receive the full amount of the contract.

At a first glance, it seems there is 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 bipartite ledger entries, it's
possible to find a path through the network similar to routing packages
In Internet."

Note: The payment channels are compostable, which means that If A and B have a payment channel, and B and C have another, A can pay from C to B. But the issue is that there is a incentive of fees for intermediaries. Now the question is what is More affordable?

(one) Doing as approach above?

OR

(two) A and C create another channel between them. Without paying B and without the need for routing. ?