lightning network – Why does the funder send the signed settlement to the counter-party in eltoo?

Quoting from the Eltoo paper:

Before signing and broadcasting the funding transaction the funder requires the other endpoint to create an initial settlement transaction that
returns the funds back to the funder. The initial settlement transaction
spends the funding output, and creates a single output that returns all of
the funds to the funder. This settlement transaction is then signed using
the settlement key and returned to the funder. The funder verifies that the
settlement transaction matches its expectations, i.e., it returns its funds and
is signed by the other endpoint. Now the funder can broadcast the funding
transaction, and wait for it to be confirmed effectively starting the contract.
The funder also signs the initial settlement transaction, making it complete
and returns it to the other endpoint.

In the last sentence, the funder signs the initial settlement and sends it to the other endpoint. But why does the other endpoint need it? This settlement transaction returns all funds to the funder, so there is no benefit for the counter-party to ever publish this first settlement transaction. Couldn’t this step be skipped?