Why do we need a "routing" process in Lightning Network? If I am wrong, please correct me.

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

So we may simplify the process of a payment between two parties in Lightning Network as follows:

(1) the sender and recipient just need to create a channel and deploy the contract and then the sender puts the recipient's address in the contract as recipient.

(2) Then any agreed number of  off-chain transactions will be done between sender and recipient such that the sender's address for each mico-payment will be verified by recipient. 

(3) Eventually, a settlement will be done via an on-chain transaction, by which the recipient will receive the total amount the contract. 

In a first view, it seems no need for "routing" process. 

So, can we now ask that why do we need a routing process for performing a payment in Lightning Network? 

P.S. I refer you to the Lightning Network website, where it's mentioned that:


  "By creating a network of these two-party ledger entries, it is
  possible to find a path across the network similar to routing packets
  on the internet."


Note: The payment channels are composable, meaning that  If A and B have a payment channel, and B and C have another, then A can pay C through B. But the matter is that there is a fee incentive for intermediaries. Now the question is which one is more affordable? 

(1) Doing like above approach? 

Or 

(2) A and C create another channel between themselves without paying to B and without need for routing ?

So, the answer of necessity of need for a routing process in Lightning Network is dependent on affordability of paying to one or multiple intermediaries instead of paying for a new direct channel without intermediary?
Even though Pieter Wuille has sad most of what was needed in the comments I will summarize this as an answer. 

Technically you could open a payment channel with every other person instead of creating a network with the ability to route. The drawbacks are that your total bitcoin amount has to be distributed over several channels and will be very small in each channel. Also creating channels with everyone would need way more on-chain transactions which would not directly help to reduce the load to the blockchain. 

--> Routing is needed to really reduce the amount of onchain transactions needed and to have higher liquidity per channel available.